The new procedure does not exclude RNAV IAPs with TAAs.

I know, but it appears it is irrelevant for TAA's.

I could have gone straight-in if cleared direct to DOCAP anywhere
within
the straight-in TAA sector. I could not have accepted an altitude of
less than 2,800 in that case, though.

And why is that? "Skyhawk 1234X, cleared direct to DOCAP, maintain
2,100 until established, cleared RNAV 18 Olive Branch."

Since DOCAP is and has always been labeled as an IAF, how is this any
different from being given MVA direct to any other IAF on non-RNAV
approaches, something that is done a thousand times every day?