This is now possible in Tor Browser 9.5: https://www.torproject.org/releases/tor-browser-95/
You can set the Onion-Location HTTP header or add a <meta> tag to the HTML.
See https://community.torproject.org/onion-services/advanced/onion-location/ and https://kushaldas.in/posts/onion-location-and-onion-names-in-tor-browser-9-5.html for details.
Yes Tor Browser does a great job of preventing DNS Leaks. Even torsock on the Linux CLI does an admirable job of preventing DNS Leaks for Linux CLI apps. I did some testing on my own with several apps and saw this for myself.
If you ever do find a DNS leak, that would be considered to be a major security hole and would be fixed ASAP.
I can't tell you all ...
Only the developers of TBB could answer your question with 100% accuracy. A couple of possible reasons include:
The TBB developers haven't gotten around to it yet -- either flipping the switch, or (probably more likely) doing an analysis of the privacy trade-offs that would result from enabling such a setting; or
The TBB developers are dead-set against ...