I have to admit - I'm somewhat baffled at the enthusiasm for a "just CAT"
softfork, since I can't see that it would achieve much. It's indicative to
me that there isn't a compelling example to date that (i) actually has
working code and (ii) only relies upon CAT. I'm not averse to CAT, just
confused that there's a lot of enthusiasm for a CAT-only fork.

To do actually-interesting covenants, afacit you'd need "introspection"
opcodes and/or CHECKSIGFROMSTACK - and even then, for almost all
applications I'm familiar with, that kind of CAT-based approach would be
much more circuitous than the alternatives that have been discussed for
years on this list.

> Vaults

I don't think this is actually a use-case that CAT materially helps with.
Andrew's posts, while well written and certainly foundational, do not
sketch a design for vaults that someone would actually use. I don't see how
CAT alone (without many auxiliary introspection opcodes) facilitates vaults
that clear the usability hurdles I describe in this paper:
https://jameso.be/vaults.pdf. For example, batched withdrawals and partial
unvaultings don't seem possible.

Even with introspection opcodes, Burak's (
https://brqgoo.medium.com/emulating-op-vault-with-elements-opcodes-bdc7d8b0fe71)
prototype wasn't able to handle revaulting - an important feature for
usability (https://twitter.com/jamesob/status/1636546085186412544).

> Tree signatures

To what extent does Taproot obviate this use?