You appear to be thinking of power only in extreme terms (possibly even as an on/off binary). Like, that your values “don’t have power” unless you set up a dictatorship or something.
But “power” is being used here in a very broad sense. The personal choices you make in your own life are still a non-zero amount of power to whatever you based those choices on. If you ever try to persuade someone else to make similar choices, then you are trying to increase the amount of power held by your values. If you support laws like “no stealing” or “no murder” then you are trying to impose some of your values on other people through the use of force.
I mostly think of government as a strategy, not an end. I bet you would too, if push came to shove; e.g. you are probably stridently against murdering or enslaving a quarter of the population, even if the measure passes by a two-thirds vote. My model says almost everyone would endorse tearing down the government if it went sufficiently off the rails that keeping it around became obviously no longer a good instrumental strategy.
Like you, I endorse keeping the government around, even though I disagree with it sometimes. But I endorse that on the grounds that the government is net-positive, or at least no worse than [the best available alternative, including switching costs]. If that stopped being true, then I would no longer endorse keeping the current government. (And yes, it could become false due to a great alternative being newly-available, even if the current government didn’t get any worse in absolute terms. e.g. someone could wait until democracy is invented before they endorse replacing their monarchy.)
I’m not sure that “no one should have the power to enforce their own values” is even a coherent concept. Pick a possible future—say, disassembling the earth to build a Dyson sphere—and suppose that at least one person wants it to happen, and at least one person wants it not to happen. When the future actually arrives, it will either have happened, or not—which means at least one person “won” and at least one person “lost”. What exactly does it mean for “neither of those people had the power to enforce their value”, given that one of the values did, in fact, win? Don’t we have to say that one of them clearly had enough power to stymie the other?
You could say that society should have a bunch of people in it, and that no single person should be able to overpower everyone else combined. But that doesn’t prevent some value from being able to overpower all other values, because a value can be endorsed by multiple people!
I suppose someone could hypothetically say that they really only care about the process of government and not the result, such that they’ll accept any result as long as it is blessed by the proper process. Even if you’re willing to go to that extreme, though, that still seems like a case of wanting “your values” to have power, just where the thing you value is a particular system of government. I don’t think that having this particular value gives you any special moral high ground over people who value, say, life and happiness.
I also think that approximately no one actually has that as a terminal value.
My model is that friendship is one particular strategy for alliance-formation that happened to evolve in humans. I expect this is natural in the sense of being a local optimum (in the ancestral environment), but probably not in the sense of being simple to formally define or implement.
I think friendship is substantially more complicated than “I care some about your utility function”. For instance, you probably stop valuing their utility function if they betray you (friendship can “break”). I also think the friendship algorithm includes a bunch of signalling to help with coordination (so that you understand the other person is trying to be friends), and some less-pleasant stuff like evaluations of how valuable an ally the other person is and how the friendship will affect your social standing.
Friendship also appears to include some sort of check that the other person is making friendship-related-decisions using system 1 instead of system 2--possibly as a security feature to make it harder for people to consciously exploit (with the unfortunate side-effect that we penalize system-2-thinkers even when they sincerely want to be allies), or possibly just because the signalling parts evolved for system 1 and don’t generalize properly.
(One could claim that “the true spirit of friendship” is loving someone unconditionally or something, and that might be simple, but I don’t think that’s what humans actually implement.)