We have been running a cryptanalysis program for Poseidon2 for almost two years now, and the plan is to continue it for a while more. It's already born fruit, identifying some important security issues in Poseidon2 (which we could solve either by adding extra rounds, or by going back to Poseidon1, which has so far stood against attacks).

If we had made a precompile, then we would have had to stick to one particular version of Poseidon, and when something like this happened, migrate to a different version, leaving a dangling precompile that nobody uses but that (like all others) contributes to unneeded greater complexity of implementing a new client, consensus failure risk, etc etc.

Once we "set in stone" a particular hash as The New Primary Hash of Ethereum, then yeah of course there will be a precompile for it.

But we are now exploring a much more practical and flexible short-term approach: a precompile that can do vector math over 32-bit numbers (think: numpy). This massively increases efficiency compared to raw execution, both because we stop over-charging by 8-64x for each operation (you don't need to pay gas for a MUL opcode whose worst-case involves big 70-digit numbers if all you're doing is 123835 * 7534622578), and because it means you only do one round of "control flow overhead" for a whole vector of numbers (size 16 in Poseidon2), instead of once per number.

This simultaneously will make it much easier to implement all versions of Poseidon, and lattice operations in quantum-resistant signatures, and lattice operations in FHE. It's basically "the GPU for the EVM", and it's not more complicated to spec than one single precompile.