By the time time people switch to ECDSA, they should switch to Ed25519 or Ed448, maybe with ECDSA fallback (with web server and TLS library support for multiple keys for same domain, depending on ClientHello).
1 - https://tools.ietf.org/html/draft-irtf-cfrg-curves-07
2 - https://www.ietf.org/mail-archive/web/cfrg/current/msg07291....