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Which happens to be QM. The next step would be matching concepts from the theory to human concepts, the extent to which that works is debatable.

I can be sold on QFT. QM is statistics as axioms and that's a harder sell.

I don’t see any difference in the concepts involved. It’s just where you start classically: Point particle mechanics -> (traditional, single particle) QM Field theory -> QFT

Then maybe we can argue about points. I think everything goes off the rails when we assume there are such places where we divide by zero.

Fair enough, but the weirdness of QM that is not due to point particles completely transfers to QFT

Quantum means discrete instead of continuous and I'm curious to know more sources from which that constraint can stem.

The most common way is the quantum harmonic oscillator, and I have no intuitive explanation for it

Let me try to bridge the gap - I've seen this start with an infinite well, and you have to start with a single central up and down between the two adjacent walls