dabac

Well, there are tire inserts, and "solid" tires. The tires aren't foam filled as such, they're made out of the same foamed polyurethane throughout.
I've logged plenty of miles on such tires. On decent roads they're a non-issue entirely. On cobbles and when crossing lane markers at a shallow angle, they're a little squirrely, but nothing critical. There's a lot more shock transfer, so you get an immense rattle every time you go off a curb or so.

If you're riding on decent roads, and is used to 5+ bar pressures anyhow, the biggest issue I can think of is to figure out which tire and pressure equivalent to go for. No margin for adjustment after the purchase.

I wanted to try inserts made for sports wheel chairs, but the guys wouldn't sell me any, claiming that they were "too hard for bike use". Obviously absolutely clueless to what regular road bike pressures are.