My suspicion is that the only reason to use cross-ply tires over radials is for historically accurate old American cars. Is that accurate?
Tisn’t. Radial tires only started appearing in the early 1950s on Citroen and Lancia models. It was a fairly slow process for them to spread to other makes, it would take until the 1970s that this kind of tire was found as standard in even the most basic vehicles, and another few years for them to completely erase cross-plies from new cars. Because the game gives you the option early on, it is inevitable that cross-ply tires are primarily used when going for a 100% period-accurate build.
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Cross ply has much lower material costs in the early years, and cars in that time period aren’t really limited by tires so much as brakes and other things.
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Even a fairly expensive euro car as Mercedes had crossplies as standard equipment a few years into the 70s.
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One thing to keep in mind that early radial tires had major NVH issues and had a reputation for lots of road noise and stiff, uncomfortable ride quality compared to cross-ply tires. All American cars and most European cars of the 1960s and earlier were also engineered specifically for cross-ply tires, and the differences in design and tuning of the steering, suspension, etc. exacerbated these disadvantages. It would make sense for Mercedes to be late to the party; handling performance for luxury cars was not nearly as important then as it is now.
Also Automation uses a highly abstracted way of calculating the cost of things that disregards marketing, economies of scale, superstitions and biases among engineers, executives, investors, and customers, and the fact that tires, too, are an industry–tires don’t grow on trees, companies have to make them. Radial tires mean entirely new tooling, retraining workers, etc. Assigning P245/45R17 tires to your 1967 sports car in Automation is easy. If you were a real auto exec in 1967 and called up Michelin for an order of 500,000 P245/45R17 radial tires, the rep would probably tell you to sober up and place a serious order in the morning because you must be very drunk. The American companies were worse–they could not produce any radial tires at all. Goodyear spent several years, tens of millions of dollars, terrified their investors, and wagered the future of the company on radial tires taking off in the late '60s and early '70s, building whole new factories and devising new production processes. If they had been wrong the costs would have ruined them.
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random fact: Late '60s Formula 1 cars still used bias/cross ply tires
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My only criticism of cross-ply (bias-ply, because 'Murican) tires in the game is the minimum 80-series profile. I believe the minimum should be 60-series for greater historical accuracy. I find myself using radials on 1960s muscle car replicas because they allow for 70-series and 60-series tires as would have been equipped during that period. An F70-14 tire would equate to a 215/70R-14 and you can’t make those bias-ply in the game.
edit: @Woolie_Wool I appreciate the history lesson. Thanks for sharing!
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Radial tires were optional on old 'Murican muscle, so it is historically accurate actually
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On a F1 track, the largest disadvantages of crossplies are probably not so noticeable. On a smooth surface, you can get good handling with crossplies, but they are VERY sensitive to irregularities in the road and prone to following them, while a car with radials will be steady in comparision. Since no regular road are as smooth as a racetrack, radials are a big advantage on road cars.
And yes, for realism, very low profiles and wide tyres should not be used too early in the radial days either. Checking out a book about cars sold in 1985 now as an example. 16 inch was only used on exotics like Ferrari 328 and Porsche Turbo, as were profiles under 60. A N/A 911 as an example had such a measly tyre by todays standard as 185/70R15, a sports sedan like the Saab 9000 Turbo 195/60R15 which was considered almost radical back then, 175R14 (82 profile) on a more regular family sedan like the Volvo 240, a hot hatch like the Golf GTI 175/70R13…it’s very easy to overdo it.
But as a rule of thumb…
1960 = Crossplies, almost universal. Very few exceptions like Citroens, but they have always been oddballs. 
1970 = Crossplies still the standard equipment on most cars, but radials starts to appear on some upmarket cars, at least as an option. I would not consider it unrealistic to use them in 1970, but choose wisely.
1980 = Crossplies almost totally gone except from a few budget cars. At this time radials definitely is the obvious choice on any car.
Considering US tyre makers and radials, IIRC BF Goodrich was one of the earliest to come out with them…
Firestone by then rushed development on their 500 radial tyre, which proved to be a bad decision, they were prone to separations and it didn’t get any better that they was standard equipment on Corvettes and such cars, so separations often happened at high speeds leading to accidents, it was a scandal and a huge recall that almost made Firestone bankrupt…
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Actually, after doing a bit more research, it turns out the first radial tires appeared in F1 in 1977. They were made by Michelin and were on the Renault RS01 (which, being the first turbo car in F1, tended to explode a lot instead of finishing) in 1977 and the Ferrari 312T* (T3? T4? not sure) in 1979, the latter constructor winning the WDC and WCC in '79. Michelin silently dominated the sport until they pulled out in 1985.
Although the F1 calendar was mostly constructed of purpose built race tracks, there were some street circuits on the calendar like Spa (which was basically a street circuit until 1970), Monaco, Montjuic, Long Beach, and racing surfaces were generally not as smooth as the surfaces today. While bias plies tended to be more forgiving when on the limit of grip, which was why 4 wheel sliding through corners was a common thing in the 60s and 70s, radials tended to be less forgiving in exchange for more peak grip. And also radials were generally more durable, so tires could be wider, which means even more grip.
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Radial tires first came into mass public choice in the 50s as they were sold and advertised through Sears Roebuck Co starting in (1954?). At first it was like a new gimmick, but with the popularity of NASCAR at the time the use quickly became apparent on sports cars at the time, however most people didn’t see the need for the extra cost of using radials over ply tires at first. As the hp, speed, and weight of American cars increased exponentially in the 50s the advantages quickly started to push car owners to opt for these tires on their Corvettes, Thunderbirds, etc. It wasn’t really until the muscle car push (mid body, large engine) craze that heated up (hence I DIDNT say STARTED) in the 1963-65) time frame that you start to see more cars with radial tires, however it wasn’t until a few years later (70-72) that you start to see suspensions TUNED for radial tires and cars coming from the factory with them. Bias Ply and Radial tires have different reflection, distoration, and must be accounted for in the suspension to avoid mis steering, over wear, etc. I have driven many post war US cars (54-59 Buick, Packard, Chevy, and Ford) as well as radial era US muscle (1970-72 Buick, Chevy and Ford). With both ply and radial tires on both. Putting bias ply tires on radial tuned suspensions is SUICIDE, however putting radials on cars tuned for bias plys makes for a slightly rougher ride (less sidewall deflection on radials) and if you have a heavy yank tank like a 59 Lincoln with manual steering it will take a noticeable more amount of effort to turn the wheel at a stop, however once moving won’t be noticeable. Bias ply tires on cars designed for them makes for a comfortable ride once you get used to the tire grabbing ‘ruts’ in the road as the ride is smoother, but get ready for tire screeching going around corners and flat spots for the first few miles if the car has sat for a few weeks or more. By the 1970s NO cars being built in the US that I am aware of were being sold with factory bias ply tires (imports possibly/likely). The only domestic new cars in the post 72 era with bias plys I could fathom would be the econo ‘shit boxes’ like the pinto, etc. No offense meant to those who relish these unique automobiles.
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