ISS is at 51° inclination...This allows for more access to it from various places on Earth (the Cape, Kourou, Baikonur) and thus more global participation to spread the risks and the costs.

True, not very effective for destinations elsewhere....But the big difference is the shuttle's payload capacity (much lower than at 28°). Expendable launch vehicles feel the difference far less (the shuttle itself has the same mass no matter what orbit).

A service station for further out....Perhaps.

But Kourou is far better located than the KSC for GEO.

The KSC is very well located (some times during a Moon orbit) for the Moon, a little less for the solar system (as the Earth's axis inclination is 23° relative to the ecliptic and the Moon is 5° from the ecliptic) .

A service station would mean a place where lots of fuel is stored (how long for cryogenics?) , lots of manoeuvres are performed (dangerous for humans right next to them) and manoeuvres also use a lot of fuel.

The fact that ISS is at 51° saved it as the Russians could keep using it after Columbia's loss.

How many spaceports other than Kourou could be used for GEO? Let's say KSC... Ok, but with some fuel and/or mass loss, too. The highest inclination for the Moon is 23+5 degrees=28° (like KSC) which is 23° less than from Kazakhstan (it's not even sure Baikonour will remain a spaceport (Vostochny is at 51°)). Kourou is 23° less than KSC for LEO (5° lat north v 28° lat north). Isn't the difference between 51 and 28 the same as between 28 and 5?

Would permanent manned operations in space be most useful for relay-stations in LEO?

I'm not sure....

Having humans in space is the result of compromises between launch ports locations, orbital inclinations and main human activities in space. No human ever went further north and south than 65° (and they were the first Vostok cosmonauts) or closer than 28° to the equator.