Fundamentally this DANE idea swaps out the problems of a PKI CA hierarchy, the kind your browser is using when you actually log into gmail to read and send your e-mail, with the problems of DNSSEC.
The biggest problems with PKI are that there are too many CAs, who can each go rogue, and that X509 is a horrifically awful format that takes a gigantic TCB to parse. Mitigations include browsers firing CAs and severely impacting their business (so effectively, there is regulation), certificate transparency and more and more testing. Either way you pretty much have to deal with these problems today though, an awful lot of e-mail is sent/received over HTTPS.
The biggest problems with DNSSEC are that DNSSEC doesn't actually protect DNS queries at their most vulnerable points, that you have to trust your TLD provider, and the root operators completely, with no effective means to fire them, and finally that they almost certainly are using embarrassingly stupid crypto that even most ICOs could avoid. This very deck has several 1024-bit RSA keys, right there on a slide with a February 2018 timestamp, as if it's not an incredibly obviously stupid thing to do since the LogJam paper was published, or you know, when everyone stopped using them for TLS years ago.
Actually wait, there's even a 512-bit key on another slide, using alg-5. That's RSA + SHA1!! What's the point of using all of those SHA256 MACs at the TLS Layer if everything depends on utterly breakable RSA plus SHA1 anyway? It's hard to take this seriously.
PS. Yes, this is also my best impression of tptacek