@JY, you know what, i have been thinking about this a lot recently, and i think we're close to being on the same page.
I think that any attempts to create a classless society have resulted in taking freedom away from people, and have created those with the power to take that freedom away ad those without, which makes two political classes (almost by definition).
So there is a part of me which doubt that a classless society is possible. I don't believe in a society where some people have the power to take from others. Which i think does leave us on the same page, or pretty close.
When i think about a 'classless' society, i recognise that human nature is not going to change over night, or over the course of a century (though our culture may change dramatically over a single century). And human nature being what it is does result in some of those 'class' distinctions you mentioned.
So let me be clear, i don't know what the ideal society would look like, or how to get from here to there, but the kind of society i'd like is one where income is not related to status, where people strive to be respected for its own sake.
Olympic athletes wok harder than nearly anyone else to be the best, and they do it for nothing but status. So i'd love to see a society where everyone has the opportunity to be the best they can be - whether as a scientist, athlete, singer, or artist. However they want to compete. And nobody feels like they are less because of their upbringing, their race, their parent's, their performance in school, or anything else (unemployed class kids who are failed by our current education system).
I don't believe in a dictatorship of the proletariate - as Marx did - in order to get there. Because i don't believe that replacing one power system with another gets you any closer... And i don't know if this is possible, but i think it is worth striving for.
So if you think taxation to pay for universal education or universal healthcare is 'taking away people's freedom' then yes. I do believe in that. But only be ause i believe the educated people who don't have to worry about affording their health care costs are more free (I would include universal basic income, if not for the fact that it acts as a negative taxation - and having the government rely on you for tax places you in a position where if the government acts in your interest they can claim more tax, thus your interest align... Negative taxation reverse this suddenly you become a liability and i don't like the idea of a more powerful state which doesn't give a shit about their population - as we already see with unemployed classes living off of the social security net in Europe, they are marginalised and ignored, as much as the government can get away with...)