I can think of some (more or less stable or scalable) societies which don't include notions of private property as generally accepted in the modern First World, but which are not totalitarian.

What do you have in mind besides kibbutzim?

A highly relevant issue here is the freedom to exit. Many small communities (e.g. religious cults) can be quite totalitarian but as long as there is freedom to exit we don't consider them horribly repressive. On the other hand I can't imagine how a totalitarian society without the freedom to exit can be anything but repressive.

We were talking about a new society, one that runs on rationality.

And who will this society consist of? Humans are not rational and do not show signs of becoming considerably more rational in the near future.

If people don't own the land, then it follows that houses should not be owned by people.

This seems to make some questionable assumptions about the relationship of immovable property to land. I've heard of traditional systems of tenure where people don't own land per se, but have claim to it insofar as they modify it or build structures upon it: you couldn't own a square mile of wilderness, for example, but you could own a house or a cultivated field.

This tends to work better in a society that runs on small-scale agriculture, where a single mode of cultivation is about all land ever gets used for, and where the amount of land you can cultivate is limited by the livestock and tools you own and the number of workers you have access to (either hired or part of your family). It'd be difficult to extend to modern land use. But it is an internally consistent way of thinking about tenure.

I don't think land should be owned by people.

By whom should it be owned, then? Or to unpack the concept of ownership, who gets to farm, or mine, or build on a given piece of land, and how will it be decided? Is the answer going to again be "somehow"? You say I'm reading my vision into your words, but that's because I'm not seeing any vision in them.

We were talking about a new society, one that runs on rationality.

I am not seeing the rationality content here.

I'm leaving the rest unresponded to, because we're both of us well into politics-as-mindkiller territory here, and I don't think prolonging the discussion is going to be useful in this venue.

ETA: But it would be polite for me to respond to your direct question, why I don't agree with caps on individual wealth. Because every honestly earned dollar in someone's hands means that they created more than a dollar's worth of value in someone else's. That is what it is, to earn money. When people pay you for what you do, your financial worth is a measure of the value you have created for them. Why cap that?

Of course, there are dishonest people, but to take away everyone's supposed excess money as a remedy is to fine everyone for the deeds of a few. And there are the practical issues of people evading such regulations by emigrating or restructuring their affairs so as not to legally "own" the wealth that they actually have control over. The dishonest are at an advantage here.

I have heard (unsourced anecdote) that when you ask people what is the largest income anyone really needs, they generally name a figure about 10 times their own. Whatever their own income is.

To me, the stories with happy people "finishing paying their college loans" are horror stories. Stories with people getting charged thousands of dollars for simple medical procedures are insane. People maximising PROFITS out of selling weapons and military technology/services... is not the mark of a sane and healthy society.

Of note: most universities are either run by the government, or by non-profit organizations. Ditto for most hospitals.