If what you are doing in your flavor-of-the-month build tool translates to a roughly equivalent number of lines in Make, then yes, you should probably look at using Make. But the thing is, Make is stupid, it doesn't know a lot. Sometimes that is a good thing, sometimes it is not.
I've written about this before on HN: I mostly program in C++ and when I build my stuff I want a build tool that understands things like header dependencies, optimization levels, shared libraries etc. It's a bonus if my build files are portable.
My point is that these alternative tools often strive to raise the abstraction level and the reason people use them isn't necessarily because they haven't discovered Make.
It reminds me of the jQuery cycle: use jQuery for everything -> decide that depending on frameworks is lame -> use "vanilla JS" for everything -> realize this requires polyfills and various other inconvenient, inelegant things -> either go back to using jQuery, or gain a much deeper understanding as to why everyone uses it.
Make is not an amazing (abit slightly bloated) meta tool that solves all your problems on all platforms (abit slowly).
The newer build tools are trying to do exactly what jquery does, and abstracting away those rough edges for a consistent build behavior with better syntax.
Going back to make is the 'use "vanilla JS" for everything' step in your list above, not the final step.
Make -> VanillaJS
Grunt/Rake/whatever -> jQuery