Why isn’t every business regulation a tax?

I'm just starting to learn about economics, so this might be a silly question, or an "if all you have is a hammer…" kind of situation, or something that works under idealized assumptions but not in practice. But I want to check where my understanding (probably) went too far up the wrong tree.

I've been reading the FAQ on carbon pricing over in r/Economics and it got me wondering: if the concept is so effective, why have any non-tax regulations for businesses at all? Why have laws forbidding all sorts of things that we deem to have a cost on society, when we could instead internalize the costs and let the market sort it out? The government could even use a negative tax to incentivize activities with positive externalities, like the education system, infrastructure, transportation, or healthcare.

I can see that this relies on a number of assumptions that will probably not hold in the real world:

• We can actually estimate the externalities somewhat accurately

• The government has enough information on the market's activities and there is little corruption, so the taxes can't be dodged or gamed

• There is strong competition (often these things are natural monopolies, for example I don't see how you could have ten competing high speed rail systems)

Is the fact that those assumptions don't really hold the reason why we don't do this or am I missing something?