Yes, and no.

I think the spirit of your argument is correct. But I find a fault in it: in reality, there is no separation between the "financial system" and "the goverment".

In way too many cases they are literally the same people, and without any known exception in any major economy in the world, they are exceptionally tighly intertwined and protect each other's interests.

So, "government regulation" is invariably in agreement with the interests of the incumbents ruling over the financial system.