This is true but seems like a problem worth solving. It's also true of more than subways; we have the same problem with bridges, housing and many other things. Better to get on with fixing it than use it as an excuse for doing something worse.
> Moreover you're going to have to close the road down anyway
That's a one-time cost, and you're not required to close a 500 mile stretch of road for years on end. Dig one block, install the tunnel, cover it, dig the next block.
IMO it comes back to the fact that Americans are just not willing to accept change of any kind right now. The economy feels too shaky, the electorate too divided (even within states and municipalities), and there's too little faith in government to architect the kind of change you'd need to build subways, underground metros, or even BRT. We need a larger feeling of unity even at a state level to make the changes necessary, which is why municipalities continue to do bare minimum maintenance of roadways and pretty much nothing else. The last big set of constriction in dense urban areas was funded by the Obama stimulus from the GFC which was passed 17 years ago.