Upon reflection I think you are right in one tangential respect - characterizing experience as "axiomatic" was a poor choice of words. For a good rationalist nothing is axiomatic, i.e. with the right data you could convince me that 2+2=3 or that A is not-A.
Nevertheless, the existence and validity of your experience as such (not to confuse this with your interpretation or memory of your experience or anything else), is an incredibly fundamental truth that has been confirmed repeatedly and never disconfirmed across a vast scope of contexts (all of them actually) and is relied upon by all other knowledge. So saying that making experience a first principle or axiom is "impractical and inefficient" is rather bizarre, unless you're talking about something completely different than I am.
[Cross-posted.]
1. Defining the problem: The inverted spectrum
A. Attempted solutions to the inverted spectrum.
B. The “substitution bias” of solving the “easy problem of consciousness” instead of the “hard problem.”
2. The false intuition of direct awareness
A. Our sense that the existence of raw experience is self-evident doesn’t show that it is true.
B. Experience can’t reveal the error in the intuition that raw experience exists.
C. We can’t capture the ineffable core of raw experience with language because there’s really nothing there.
D. We believe raw experience exists without detecting it.
3. The conceptual economy of qualia nihilism pays off in philosophical progress
4. Relying on the brute force of an intuition is rationally specious.
Against these considerations, the only argument for retaining raw experience in our ontology is the sheer strength of everyone’s belief in its existence. How much weight should we attach to a strong belief whose validity we can't check? None. Beliefs ordinarily earn a presumption of truth from the absence of empirical challenge, but when empirical challenge is impossible in principle, the belief deserves no confidence.