People can already choose what kind of certificate they want issued to them, because the CA does not generate your private keys. Them giving you a certificate

People can already choose what kind of certificate they want issued to them, because the CA does not generate your private keys. Them giving you a certificate with an RSA public key in it is impossible if you submit a Certificate Signing Request with an ECDSA public key in it (or vice versa). Then it's only down to what intermediate certificate you want to serve. That's the constraining factor; since you don't get to choose which private key the CA signs your certificate with, you have to use the intermediate certificate whose public key corresponds to the private key that made that signature. The sensible thing for a CA to do is to sign with (and supply) an ECDSA intermediate if they get handed an ECDSA CSR, and an RSA intermediate if they get handed an RSA CSR. I imagine this is what Let's Encrypt does already.