We implemented a generic NTT in Yul, with examples provided for DILITHIUM and FALCON fields and reduction polynomial here:
Compared to available implementations, we cut FALCON gas cost from 24M to 3.6M, more optimizations being still WIP. However we are quite confident in the fact that it cannot be cut below 2M considering the number of required operations. As such going RIP/EIP is necessary for day to day transactions.
We believe that NTT has separate interest (speed up STARKS settlements, implement any lattice candidate) and proposed a related EIP: