In the old days -- like 1997 when I got my GMRS license... Base stations couldn't even talk to another base station (besides having only two of the 8 main frequencies assigned).
You have to look at the original GMRS intent: family or small business (the latter are grandfathered, but no new business uses are being licensed). In the case of the "family" -- think a moderately large farm. The base station would be in the farm house, while the family working the fields are using HTs or mobiles. Even a 640 acre farm is only 1x1mile -- and being a farm is likely flat enough that even a 2W HT could go corner to corner (1.4miles).
Now... the tricky configuration: a repeater WITH microphone and speaker, located at the farm house. It would receive on the 467MHz frequencies, but only transmit on the 462MHz. This would qualify as a base station (think of it as a Dispatch operator, sending directions to scattered family members) when using the microphone/speaker, yet be a repeater for really wide spread family.
Given the limited number of /shared/ frequencies in GMRS, and the prohibition on digital data (except for low power HTs sending location data on SIMPLEX frequencies) I don't think there are many "fixed stations" in GMRS -- unless part of a grandfathered business license. I think of fixed stations as things like telemetry or relays (not repeaters), possibly using DTMF tones to send/receive commands. "Fixed" stations don't "talk" to general public -- they use directional antennas (YAGI, dish...) aimed at another fixed station.