The problem with Make, is that it works just well-enough to allow people to sorta get it to work without requiring them to learn how to actually use the thing. Then they don't read the manual, and complain that Make doesn't, in fact, work.
Make is full of this stuff and as a distro packager having to deal with each's individual quirks is prone to drive one insane. Please consider using meson, at least.
I prefer to just run "make clean" after I delete, rename or move source files.
With a properly written "Makefile" nothing else needs to be done and there will never be a broken build. With a properly written "Makefile" nothing has to be done when adding source files.