> The way to do that requires them to know that the key which signed the data belongs to you.

This is something S/MIME does and I wouldn't say it doesn't do so well. You can start from mailbox validation and that already beats everything PGP has to offer in terms of ownership validation. If you do identity validation or it's a national PKI issuing the certificate (like in some countries) it's a very strong guarantee of ownership. Coughing baby (PGP) vs hydrogen bomb level of difference.

It much more sounds to me like an excuse to use PGP when it doesn't even remotely offer what you want from a replacement.