Does this example of a bad government regulation come from the government? Or the people voting and demanding it from the government?
No, it comes from business. DMCA is an example of the badness of private business if allowed to do what it wants.
That was a purchased law. The failure on the governments part was in allowing itself to be for sale.
So you are right, even though I bet this is just about the opposite of the conclusion you thought citing the DMCA resolves out to, we should definitely stop allowing the government to be influenced by the private sector.
That's tautological statement. There is no free market without private property protections which do not exist outside of government regulation either.
Government protecting people's rights, vs. government protecting people, or government prohibiting consensual business dealings.
You don't have to fall for it, though.
The monopoly on force which defines the state must first form before there can be any government regulation, and thus must inherently form outside of government regulation.
Once that forms, of course, there is virtually no example of anything in human society forming outside of government regulation.
But taking the absence of evidence of how things behave “outside of government regulation” for evidence of ones preferred view of the difference between life under government regulation and without it is rather unwarranted.
Facebook has a monopoly on the social network.
There is certainly the danger of regulatory capture that increases the costs for competitor to enter a market, but that is different than regulations on how large corporations are allowed to wield their power as market leaders. You need to distinguish between regulations that increase the costs for new competitors vs. those that prevent bullying/price fixing etc. For example, it was anti-trust regulation that gave rise to popularity (not initial creation) of Unix, and interoperability regulations that further expanded competition in the telecom industry.