Alright, so what I did is add the following to my ~/.profile.

--8<---------------cut here---------------start------------->8---
if ! command -v cc >/dev/null 2>&1; then
	if command -v clang >/dev/null 2>&1; then
		export CC=clang
	else
		export CC=gcc
	fi
fi
--8<---------------cut here---------------end--------------->8---

Now I can run `make` and it works as expected for projects that don't define CC.

-- 
Pierre Neidhardt
https://ambrevar.xyz/