Hrrumpt The Gnu C compiler was starting to be available by the mid-1980s in alpha/beta form. rms was looking for places to start. He approached a number of folks, from Tanenbaum to some of the vendors (he knew Masscomp had written a compiler from scratch which we away the binaries gave to our customers and he called me asking if we would donate it. We had donated development hardware and I was still his contact to the Gnu project at that point).
As far as I know, he ended up writing his own because he could not find one to start with. The big kickstart for rms, was that Sun hard just started to charge for its compilers, and so a lot of people were looking for a free alternative (and frankly in those days the Sun compiler was still a bit of a toy -- 20% we got over them at Masscomp was because we had a number of the folks from the DEC compiler team).
It is true that the targets and the original systems it ran were more limited. The 1.0 release was before the summer of '87 (in May maybe???). The biggest issue is that it did not run on DOS until the 386 and the DOS-extenders show up. But it covered the many 68000 workstations and was often as good or better than the supplied one [which were mostly based/derived from the MIT Jack Test port of the Johnson compiler for the NU system].