Yes and no.
I think you are correct when we apply all you said to everybody involved in politics. They indeed want power no matter the cost (to somebody else). There are also politicians who indeed believe honestly and sincerely in all the statist/socialist/welfare-state crap. That’s not to say that they don’t clamor power to implement their ideas. There are sincere leftists who think they love America and believe that America would be better if humbled with a bloodied nose. So they were advocating for defeat in Iraq and Afghanistan, etc. To me they are dangerous idiots, but they can kill me if I say that they are less patriots than you and I.
There are also all that people who bring the left to power by voting for them. All those people don’t get power themselves (only lousy handouts at best), but they believe in socialist ideas of egalitarianism - equality of result. It’s a wishful thinking of course, but there lies the power of socialist ideas, their undying attraction: they require no proof of success in reality, just wishful thinking, and there always will be enough of fools to believe that that’s enough.
Yes, the topic did cover a lot of ground. I was addressing the case of those in positions of power, who are verifiably not interested in “equality of results” if it affects themselves.