It's somewhat less constructive than reinventing the wheel, actually. It's axiomatic, not empirical.

The whole von Neumann-Morgenstern edifice (which is roughly what Psy-Kosh seems to be reconstructing in a roundabout way) is axiomatic. That doesn't make it worthless.

assigning utilities to different outcomes such that they maintain preference ranking ...could be done about as well with [the assumption that] all outcomes can be mapped to discrete util values.

Well, yes. You can derive X from the assumption that X is true, but that doesn't seem very productive. (I didn't think Psy-Kosh claimed, or needs to claim (yet), that all utils are measured on the same scale, but I could be wrong. Not least because that statement could mean a variety of different things, and I'm not sure which one you intend.)

Only some preference orderings can be represented by a real-valued utility functions. Lexicographic preferences, for example, cannot. Nor can preferences which are, in a particular sense, inconsistent (e.g. cyclic preferences).

My sense is that Psy-Kosh is trying to establish something like a cardinally measurable utility function, on the basis of preferences over gambles. This is basically what vNM did, but (a) as far as I can tell, they imposed more structure on the preferences; (b) they didn't manage to do it without using probabilities; and (c) there's a debate about the precise nature of the "cardinality" they established. The standard position, as I understand it, is that they actually didn't establish cardinality, just something that looks kind of like it.

Intuitively, the problem with the claim that utility "indices actually correspond[] in a meaningful way to how much you prefer one thing to another" is that you could be risk-averse, or risk-loving with respect to welfare, and that would break the correspondence. (Put another way: the indices correspond to how much you prefer one thing to another adjusted for risk - not how much you prefer one thing to another simpliciter.)