Maybe. In the middle scenario where most first-to-recursive DNS calls are DPRIVE but the authoritatives overwhelmingly aren't you get free security by just checking the "use DNSSEC" box and so browsers may just begin doing that, maybe gradually or maybe as a result of a headline making incident. See also the curious case of TLS_FALLBACK_SCSV. (Basically if you don't implement SCSV then unsafe fallbacks are too dangerous to attempt, but anybody implementing SCSV doesn't need an unsafe fallback anyway, so, forget this new protocol feature just never do unsafe fallbacks, duh)
Once you're checking that box, DANE is almost free. Egos involved may determine that it's important to never technically do DANE, so as to save face, see also why TLS 1.3 isn't just named SSL 3.4 or SSL 4.0 even though that's what it "is" in some sense. But the effect, yes. If that scenario plays out it's what will happen.
One blocker for DNSSEC and thus DANE was deployability difficulties facing middleboxes. But middleboxes have choked so much else since that today "defeat middleboxes" is just table stakes. It was needed for TLS 1.3 and it's needed for QUIC and for HTTPS DNS records and... if you're defeating middleboxes anyway you might as well have DNSSEC.
It makes sense to expend the effort to defeat middleboxes when what you win is QUIC or TLS 1.3, both of which work immediately on the Internet today. It doesn't make nearly as much sense when the payback is DANE, is supported almost nowhere --- significantly less than 2% of domains.
This isn't a chicken-and-egg problem: domains can DNSSEC-sign now, without any middlebox interference, and overwhelmingly choose not to.
It is a chicken-and-egg problem though. DNSSEC requires additional infrastructure, especially for key rotation. Yes, it's not that hard (I set it up for the domains that I control) but it's also not just a record that you can set once and forget. It is beyond unsreasonable for widespread DNSSEC support from domains when browsers have been dragging their feet for years. There needs to be an actual benefit that comes with setting up DNSSEC before most will do it.
