It seems Tk tries to compile its own libpng if it can't find an existing one. The libpng needs some header files that don't exist on the modern macos, so the installation fails.

By running

brew install pkgconf
[download]

I installed pkg-config which made it possible for Tk to find libpng and everything worked.

I also installed

brew install libpng
[download]

but I'm not sure it's needed (didn't have enough time to experiment with it).

(Read all the replies here and links from them elsewhere to get the context).