It's not about proving that you can serve HTTPS, it's about proving that you can legitimately serve HTTPS. I'd find HTTP(S)-based validation ok if CAs wouldn't

It's not about proving that you can serve HTTPS, it's about proving that you can legitimately serve HTTPS. I'd find HTTP(S)-based validation ok if CAs wouldn't issue certificates with an expiration time past the expiration time of the DNS records. Of course that would be fairly impractical. But then DNS-based validation exists and doesn't have these problems.