Regulations are needed to keep people and companies from burning the commons, and to create more commons.
I would add that in modern society, the state is the entity tasked with protecting the commons because private for-profit entities don't have an incentive to do this (and private not-for-profit entities don't have the power). Moreover, it seems obvious to me that stopping dangerous AI should be considered a part of this commons-protecting.
You are correct that the state's commons-protecting-function has often been limited and perverted by private actors quite a few times in history, notably in the 20-40 years in the US. The phenomenon, regulatory capture, corruption and so-forth, have indeed damaged the commons. Sometimes these perversions of the state's function has allow the protections to be simply discarded while other time large enterprises to impose a private tax on regulator activity while still accepting some protections. In the case of FAA, for example, while the 737 Max debacle shows all sort of dubious regulatory capture, broadly air travel is highly regulated and that regulation has made it overall extremely safe (if only it could be made pleasant now).
So it's quite conceivable given the present qualities of state regulation that regulating AI indeed might not do much or any good. But as others have note, there's no reason to claim the results would be less safety. Your claim seems to lean too heavily on "government is bad" rhetoric. I'd say "government weak/compromised" is a better description.
Even, the thing with the discussion of regulatory capture is none of the problems describe here give the slightest indication that there is some other entity that could replace the state's commons-protecting function. Regulatory capture is only a problem because we trust the capturing entities less than the government. That is to say: if someone is aiming for the prevention of AI-danger, including AI-doom/X-risk, that someone wants a better state, a state capable of independent judgement and strong, well-considered regulation. That means either replacing the existing state or improving the given one and my suspicion is most would prefer improving the given state(s).
TL;DR: I am rather confident that involving governments in regulating AI development will make the world less safe, not more, because governments are basically incompetent and the representatives are beholden to special interests.
Governments can do very few things well, some number of things passably, and a lot of things terribly. We tolerate it because the alternative is generally worse. Regulations are needed to keep people and companies from burning the commons, and to create more commons. The environment, infrastructure, public health, military, financial stability all require enforceable regulations. Even there the governments are doing pretty poorly (remember FDA, CDC and their siblings in other countries, as well as WHO?), but having a free-for-all would likely be worse.
How the proponents of AI regulations expect it to go: the governments make it hard to hoard GPUs or to do unsanctioned AI research, or to use the whole internet to train the model without permission. Sort of like HIPAA in the US makes it harder to obtain someone's personal health data without their permission.
How it is likely to go: Companies will be pretending that their all new more capable and more dangerous AI model is just a bit improved old model, to avoid costly re-certification (see the Boeing 737 MAX 8 debacle).