The wording of your question implies that this would somehow be easier than what we have now, but the reality is quite the opposite.
Firstly, DNS as implemented today is strictly hierarchical. That puts constraints on how DNS records can be signed, because you need to trust every zone back to the root not to have been substituted. This is rather different from the ability to prove ownership (or at least control) to any third party, as is done with domain certificates.
Secondly, IP address allocation is complex, and often dynamic. A certificate for ownership of an IP address would need a short lifetime, and to be obtainable at short notice. There's also a question of how exactly ownership would be proven to the certifying authority.
Assuming these difficulties were overcome, you've still got two systems of signatures instead of our current one. While a more secure DNS would be beneficial for issuing certificates, an end-user checking the connection in our current system doesn't need it. If the DNS record is forged, it will point to a server which doesn't have a valid certificate for the requested domain, so the connection will be rejected.