In Mercurial, you can kindasorta have this if you do all your development on named branches, and only merge the named branches back into the default branch at these significant moments. Then, you can merge willy-nilly, without rebasing or otherwise destroying or lying about history, and distinguish ignorable work-in-progress merges from significant feature-complete merges by which branch they were on. Most query commands let you filter by branch, so you can easily do that.
For those not familiar with Mercurial, the difference that allows this is that Mercurial permanently records the name of the branch a commit was added to. That means there is an observable difference between merging A into B and merging B into A. This is not universally agreed to be a good feature, but it does allow this particular approach.
Then you just have to choose between having a single shared development branch, a branch per developer, a branch per story, a branch per task, etc, and come up with a coping strategy for any resulting proliferation of branches.