In this case git can do the same thing, but notice you can only do it because git provides a special command for getting that revision. Recasts are really general (a greatest common ancestor function is provided, but can be easily synthesised from more primitive building blocks) and can be used everywhere, so you can bisect over changes you made that touched files matching a pattern, or whatever. They aren't something I use every day, but they are really useful on occasions and allow for some pretty robust tooling to be written.
This requires using bash. I find it kind of cheating that git ships bash on Windows so that Windows users can rely on bash for composing git commands. I'm not sure if Windows users are generally that happy about typing bash commands, but I guess nobody really cares what you have to type in as long as it's high in the Google hits for whatever operation you want to perform.
Mercurial's API (i.e. the CLI) makes a point of being usable with powershell and cmd.exe, which I think some Windows users appreciate.
Another way to look at this is that hg needed to bake this into their core, whereas git didn't need to. There is a non-zero cost to all additional code, so leaning on the shell to do work is generally a smart move.