* DANE is effectively a key escrow system. COM's keys would be held by the USG.
* In the same vein: people with cosmetic TLDs like .LY would be forced to concede their TLS policy to governments like Libya. Similarly: the Internet would be conceding that protocols should work differently and be less trustworthy depending on what country you're in.
* The "last mile" on DANE is spoofable, because DNSSEC doesn't protect the link between browsers and DNS servers; it's a "server-to-server" protocol. In particular: your ISP could still override pins!
* DANE doesn't actually work in practice, because of all the networks that block odd-looking DNS lookups; this is Adam Langley's point from "Why Not DANE In Browsers".
* Stale or misconfigured DNSSEC signatures knock whole sites off the Internet with no diagnostics. Unlike a broken HPKP pin, there's no UX saying something's wrong with the site; it just doesn't exist anymore. This is what happened to HBO Now on Comcast, and why Comcast users occasionally can't reach .GOV sites (which mandate DNSSEC).
* DNSSEC is far, far more expensive to deploy than HPKP (HPKP is just a header you add to your web server configuration).
* The cryptography behind DANE is 1990s-grade. The DNSSEC roots are still RSA-1024! (Don't worry! They've got the upgrade to RSA-2048 on the calendar!)