Yes, DNS is good enough for organizations (though I should note that governments don't rely on DNS registrars, they run their own). The crucial difference is that organizations can hire people to care about those things, or hire lawyers to ensure they can be recovered if accidentally lost. And in fact many of these organizations change domains in the longer run for various reasons. So even there, DNS is often only used as a solution to identity at one point in time, it's not meant as a permanent solution for the entire life of an organization.

For individuals, the cost of losing your domain is far too high if it means losing your identity on multiple services at the same time. And, if nothing else, people eventually die, so domains will be lost by their original owner and then re-used, breaking the notion of identity again in the longer run.