Indeed. But FIPS is not the only problem. Both the McGrew/Viega spec and subsequent NIST spec of GCM mandate a 4-byte counter - any departure from that would be "no longer GCM".
Is the argument for a small counter that nobody serious will treat it as a significant diversification component or reliable source of entropy, especially in a streaming mode? It's a counter whose function is necesesarily finite and predictable (and reversible?), if not explicitly linear. Intuitively, any substitutions or convolutions derived from it would weaken subsequent operations, no?