Can ZKP support make PQC schemes more block space and validation time efficiency?

My understanding of PQC (post quantum encryption) schemes is that it usually requires one or more of the following:

1. Very big public key
2. Very big signature
3. Very slow verification time

This allows for when you want to keep the node validation resources constant (i.e., if the block size does not increase and you do not allow a significant increase in the worst case block validation time).

Furthermore, although a (hardware) wallet that generates such signatures may have to be more powerful, I’m not worried here.

At the same time, there is a lot of excitement about ZKPS (Zero Knowledge Proof) in terms of space efficiency and inexpensive to verify.

Both PQC and ZKP require future soft forks to be practical for individual use.

This asks the question whether these can be combined. If Bitcoin has a soft fork that makes ZKP practical, using direct OP codes or with efficient contract support, can it be used to implement PQC?

I can imagine at least two warnings.

1. ZKP selection adds additional encryption assumptions
2. If ZKP (contract) is based on challenge response, the worst case footprint is still an issue

But is that all?