Is the "nothing at stake" problem exaggerated?

Given a rule that (blockheight-skipped) is treated equivalent to "length" or "total difficulty" in proof-of-work, and assuming fixed slot time, the validators will converge on the chain that has the majority of validators. Any attempt to somehow build on an infinite number of forks because double-signing is possible (whereas in PoW it is impossible) will not lead to the honest majority following along, as those "alternative forks" will never become the "longest" (in terms of least skipped) chain. So in order to actually pull of an attack based on that you have "nothing at stake" you need to be the majority, i.e., >51%. Whenever you are the majority, you are already free to attack the network as you want as nothing protects it against 51% attack, the security model in Nakamoto consensus (or traditional solution to Byzantine Generals Problem) is an honest majority. Given this, you can also notice that the reason Satoshi used PoW was not because double-signing was impossible, it was probably primarily because it has random validator selection built in (whereas with proof-of-stake you need to also solve random number generation), and much like the ancient Greeks Kleroterion it is the "democratic lottery" that was the basis of Nakamoto consensus. Bootstrapping a proof-of-stake system back in 2009 would have been a lot more complicated. From that you can notice that those who shouted about "nothing at stake" because "there was something at stake in PoW" may have misunderstood things, they assumed the "no double signatures" was somehow essential but it was probably not the feature that made PoW ideal for a first version of "democratic lottery" to control a computer platform.