Provided they are launched in the US, on a US-owned carrier? Most likely

Can't necessarily stop a multinational firing things to space on Russian/Chinese/ESA launch vehicles

Maybe but if so, it would mean that US spontaneously would go against one of their main strategic interests for the planet ? Doesn't makes too much sense.

It's like this bicycle meme where the person puts a stick in its wheels.

It's for the same reason that petrol cars are encouraged in the US.

Punishing SpaceX will lead to a bigger financial crisis, an upset Elon Musk who might refuse to fund the next democratic election and dozens of thousands of lost jobs (fortunately they already became millionaire, riding the right rocket) for a problem that most of the rich population doesn't care about.

Because in the city, it's about your petrol car, big trucks, and nobody to see the stars and a bit more pollution doesn't change much at that scale from their eyes.

CFCs (these gazes destroying ozone) were a notable exception, because it would lead to death of everyone (the same way that petrol with lead), except death, universally there was no advantage to defend.

But a space filled with US satellites is a great advantage for the US, since they are the only ones with the capabilities to deploy thousands of them, and it's a big business for military intelligence.

I can imagine the main reason they are going to regulate, is so that older satellite debris don't destroy the new shiny satellites, but beauty of the sky is going to be the very least important factor.