What's hilarious/sad to me is that Kiln started out (as the prototype that won Django Dash) doing only pull requests. That was literally all it did. Pushing directly to a repo would instead, behind-the-scenes, make a branch repo and put your commits there. When you accepted the review, it'd automatically get merged. Kiln would even warn you if you could safely do the merge without conflicts. This was all back in 2008, and I believe predated GitHub launching entirely, but certainly predated PRs being common.
Hilariously, we concluded internally that doing things that way was too complicated/weird for people to use, while GitHub concluded the exact opposite, and the rest is what you see.
True. As a workaround you can bridge your feature branch workflow to Kiln reviews by using the kiln extension locally with the push command to attach the changesets to a review, as in:
hg push --review -r [REV|BOOKMARK|BRANCH]
Bitbuckets code review implementation doesn't handle big changes gracefully though, so I primarily inspect the changes in Beyond Compare.