The reason we don't have DANE support in browsers is of course because Google decided not to implement it in Chrome, because (ultimately) the key lengths securing the root DNS server zones weren't large enough to suit them (at the time, 1024 bits):
https://www.imperialviolet.org/2015/01/17/notdane.html
And if Google wasn't going to do it, it didn't make sense for any other browser to do it either.
However, I believe the root zone keys are now longer, so I could (potentially) see Google implementing DANE in Chrome now, maybe with a Chrome-specific restriction of "TLSA records that have keys under 2048 bits in their chain of trust are ignored" (since the root zone keys are not the only keys in the chain and they want to eliminate 1024-bit RSA from Chrome). And if Google does it in Chrome, then everybody else has to do it too, so the situation flips.
More to the point I would trust IANA and ICANN, faults and all, to not screw up the DNS/DNSSEC root, much more than I trust every CA in the default browser trust stores to get X.509 right all day, every day.
I think that's for the best; there are much bigger problems with DANE/DNSSEC than TLS reliability.
Fortunately, the WebPKI has been ratcheting (slowly) up security over the last 15 years, so when nothing else happens, which is what I predict, at least we'll be in a better place a decade from now.
But let's whiteboard for a bit: if you agree (as I assume you do) that the current situation is at least more insecure than it should be, and should ideally change fundamentally, and if you don't think DANE is the right fundamental change, what would you implement instead if you had the magic wand to make everyone agree to do it?