Although GNU make does come with an automake environment, it also provides a shell script that
can be used to build make. Obviously this will recompile and relink everything every time you
run it, but GNU make is not such a huge program that this is a problem. And once you've got
it built once, you can use that make for subsequent builds. Having this avoids the catch-22
of needing some make to build make.
That said, automake is awesome especially if you're developing highly portable tools, which
most of the GNU tools are. For GNU make I don't so much care about the portability aspects,
although that's nice too (but the shell script above would be enough of an "out" for GNU make
itself). The great thing about automake is all the default rules it provides, including
things like distcheck for building new packages, etc. These rules save huge amounts of time
and effort for package developers/maintainers.