Is it possible to create a Dilithium Prime or Falcon Prime?

In the NTRU Prime submission, principle author, the well-known DJB is adamant that

[the] primary objective [of NTRU Prime] is to eliminate unnecessary complications in security review

So much so, to the extent that the idea of pure cyclotomic ring, module, decryption errors, etc. are exterminated from the design.

I think this is good, as NTRU Prime serve as a model alternative to the other designs from the finalists. I'm convinced by various arguments he made in the presentation at the 3rd PQC standardization conference.

But what about digital signatures?

• What if any of DJB's choices made in eliminating unnecessary sec-review complications applies to, or is justified for digital signatures?

• Or from the other side of the perspective: are there design decisions made in Dilithium or Falcon that can be justifiably deemed problematic according to DJB's methodologies?

• Is it possible and meritful to adapt some of the NTRU Prime design decisions and strategies to either of the lattice signatures from the finalists?

• What if any of DJB's choices made in eliminating unnecessary sec-review complications applies to, or is justified for digital signatures?

• Or from the other side of the perspective: re there design decisions made in Dilithium or Falcon that can be justifiably deemed problematic according to DJB's methodologies?

An analogous of decryption failure in Dilithium, would be the use of hints for compensating dropping over half of lower bits of public-key component $t$. qTESLA took the idea from Dilithium in round 2 and got itself broken.

As for Falcon, it once had some implementation bug in the Gaussian sampler, which amounts to a security concern and mis-estimate of instance parameters. The general design pattern of Falcon can be described as sophisticated, contrasting with many of DJB's work (e.g. Salsa/ChaCha-20, Curve25519, etc.) which can generally be described as simple and consistent.

• Is it possible and meritful to adapt some of the NTRU Prime design decisions and strategies to either of the lattice signatures from the finalists?

It should be clarified, that, it's not design elements that should be adapted to either of them. Arbitrarily applying an element over existing one provides little to no overall benefit.

Rather, it's the simplicity and consistency may be applied to their design, to eliminate exceptional elements.