You can get foam filled tires for bicycles, lawn mowers and tractors, but why not on cars?
I don’t know about foam filled tires for tractors.
All the agricultural ones I’m aware of have their tires filled with water to improve traction.
Racing bike don’t have foam tires either.
I would expect the disadvantage with a solid foam tire compared to a pneumatic tire is its capability to deform when cornering at speed and maintaining contact with the road surface.
Last time I checked, it breaks down with repeated heating cycles and is too heavy.
I have to admit, I probably haven’t looked into it in 20 years.
I suspect there would also be problems with heat retention. Too much heat could build up resulting in delamination of the tire structure at high speeds.
They don’t use them for cars because foam tires kinda suck. They don’t deform like pneumatic tires, so they give a harsh ride and have poor traction. For a riding mower or a tractor this isn’t that big of a deal, but even for a bicycle foam tires give poor performance. Go over a big enough bump on a bicycle with foam tires and the lack of an air cushion may mean that you ruin your bicycle rim.
Scale up to a car’s size and weight and the harsh ride and traction issues get really bad.
Foam tires are also difficult to install and remove.
The big advantage for a car would be that you could drive over nails and all kinds of road hazards and the tire would never go flat. For cars, there are better run-flat technologies out there that don’t totally ruin the car’s ride and handling.
Sounds like a non-starter for a car tyre as what would be the motivation? Miles heavier, less safe due to poorer grip and handling [could be far less safe in the wet], harder to fit, possible stability problems with the material over the operating speed and temp of the tyre as other posters have said above. Probably several other awful features I’m not thinking of.
They would probably be more durable and couldn’t puncture, but is flatting tyres a problem for the vast majority of drivers on tarmac roads? I mean it happens but it’s rare. I’d rate not driving the car into a ditch on a rainy evening as being somewhat more important.
There’s a lot of innovation in materials and I know that solid bike tyres have improved a lot - they were life-threateningly shite when they were experimented with years back, and now they are average. Not something you would put on any serious bike, but you see them on city hire bikes and they are fine for that, and it’s a good idea to puncture-proof that sort of machine for bicycle riding.
Maybe we will see something like for city cars as driving habits change? If we’re all scooting round the city in electric motors and materials keep advancing.
As an aside - As I’m typing this a delivery guy has just handed me a graphene tubular bicycle tyre - 200x stronger than steel, 1 atom thin, 10% energy reduction, self-healing! [sadly it’s largely marketing bollox in this instance, but it’s still a great tyre] The automotive industry dwarfs the cycling industry, so one would assume there are serious levels of R&D continuously going into car tyres.
Foam-filled has been tried but fell short. But pneumatic rubber could be replaced with urethane and composite materials. The tires are mainly hollow containing internal urethane ‘spokes’ and unpressurized air. It will be hard to displace rubber tires in economic practicality because of the incredible number of them already produced and the economy of scale.
though initial applications are for low-speed vehicles. Looking at them, I can’t see them having sufficnient lateral strength or stability for higher speed cornering loads.
“Run-flat” tires for cars have been around quite a while, more than 10 years. I have a 2007 Corvette with RFs and they came from the factory like that. If we had to carry a spare, it would take up most of the room in the trunk, not to mention that front and rear are different sizes.
The RFs handle quite well (I don’t think most use them for racing though) and are as good as any other conventional tire, but some brands can be a bit noisy. How they work: The sidewalls are very thick, and if the tire goes flat they are stiff enough to hold the car up. People who’ve had them go flat say they couldn’t even tell the difference, handling-wise. Of course you’re supposed to keep the speed down and try to get them fixed/replaced within 50 miles or so.
Now as to why my construction wheelbarrow has a pneumatic tire? – I have no clue. That is the height of stupidity. They can go flat, they can leak requiring you to pump them up periodically, and I think it would “handle” just fine with solid or other non-pneumatic tires. 
Bridgestone has been trying to make non-pneumatic tires (but not foam-filled) for years but they just don’t work like air-filled ones. I imagine a lot of the problems with physics is the same with foam-filled.
Cost. I happened to buy a new $75 wheelbarrow last weekend. An identical version with a foam-filled tire was $95 (which I would have bought but it was out of stock).
And my /oldest/ wheelbarrow actually doesn’t have a pneumatic tire. Solid rubber strip on a low-profile 
wheel. No doubt that’s one reason it’s still in use, when others have long ago been discarded.
Those look a little different from the ones I saw a promo for that had the radial ‘spokes’ internal to the wheel. They would have radial belts and cords built into the tread just like common tires, and urethane has been shown to be a workable substitute for rubber in pneumatic tires so it’s just the ability of those ‘spokes’ to hold up as well as compressed air does that would be different.
My wheelbarrow is probably an expensive collectible by now. I bought it (used) in the mid-'70s. :eek:
I had to replace the tube some years ago, and the new tube (made in China, of course) leaks slightly. :mad: