May want to look at Just. It is heavily inspired by Make and shares much of the same syntax, but removes a lot of the workarounds necessary to use Make as a task runner and adds a few other features.
It's a little more user-friendly, but not enough to justify how much power you lose.
I spent the last 20 minutes reading Just's documentation, and it seems like the only real wins are nicer argument parsing and && dependencies, and the --list argument. And in exchange for that, you lose file-based dependendicies and Make's powerful templating engine. Did I miss some other features that make the trade worth it?
Even for a Makefile, "start", "test", "install" are likely to be phony (and not literally refer to files with those names).
The execution of a "start" task defers the role of "has it already been done" to other places.
One way of describing "task runner" is "nicer UX for .phony targets".
From Make's point of view, they're just target names. Make doesn't care whether or not a target produces any files. Targets can satisfy dependencies for other targets, as can files on the filesystem.
But often tasks are a step removed from that. Targets like "all" and "clean" are good examples of useful tasks to have, even if they're unrelated to files.
A "task runner" isn't intended to replace all of a Makefile's functionality. It takes a common use case of Makefiles, and improves the user experience for this.
I think it's fair to say that it's not a big step up; but it's a definite improvement for what it does aim to do.
But if you ever get to a point where you _want_ to express some source-code dependencies (say: pip-install depends on requirements.txt), you can also do that in Make. Just doesn't provide any mechanism for it.