the boundaries would be equidistant when each outlet was at the same height.
In some instances that is the case.
In others, while placing a boundary midway between the coverage of two VHF outlets may be a starting point (and may in fact be left as just that in some areas, particularly remote), the locations of ADs then are taken into account. It may then be the case to have a boundary capture an AD in a particular FIA so that aircraft on the main route(s) to that AD stay on the same FIA freq. rather than transfer to another for the last portion of the flight.
Traffic on particular air routes is also taken into account e.g. to capture a particular air route in one FIA and not have crossovers.
VHF coverage in the circuit area of ADs is taken into account where possible. Situations where comms are available in the circuit on a different (adjacent) FIA freq. but not on the one the AD lies in are avoided.
And if an ATC sector boundary is involved, it may be that an FIA boundary is aligned with that, to again avoid crossovers into another sector,
or an ATC sector boundary may be moved to align with an FIA boundary, to take account of all the above.
Each situation is different with different factors, and boundaries placed accordingly.
The bottom line is that FIA boundaries are not placed solely due to ATC workload.
Here endeth the lesson ........ are you gonna pay for all this??