Once confirmed in a block, signatures don't need to be checked again, even by new nodes, so it doesn't need to be saved.
That contradicts the trustless principle of Bitcoin.
In Bitcoin the idea is that a full node only trusts itself so it verifies everything, that includes signature verification. If you just trust the other nodes and PoW, then you can no longer call your client a full [verifying] node and you might as well run a SPV client (eg. Electrum) which is so much easier to sync and consumes less bandwidth and disk space.