It wouldn't need to turn as fast to stay focused, maybe increasing the lifetime of its reaction wheels.
On Earth when you "turn" a telescope, you are really keeping it pointed in one direction! It's the Earth that's turning, and you have to turn the telescope mount to keep the legs pointed at the ground.
It's the same thing as having to move the antenna to keep it pointed at the ground!
As an aside, how do space telescopes handle pointing antennas at earth?
GAIA uses a phased array that can always beam towards earth as the telescope rotates (see this answer), and TESS stores, compresses and processes almost two weeks of data while measuring near apoapsis, then zooms past Earth and sends it in an 8 hour burst during periapsis. (See this answer and this answer).
In space you don't turn a telescope, you leave it mostly alone and it nearly keeps pointing in one direction. There are small tidal forces especially in LEO (see this answer), and other torques like solar pressure (see this answer) that will very slowly tilt a telescope, so the reaction wheels have to handle that.
But there is no major space-telescope-turning necessary to compensate for Earth's rotation. That's strictly an "Earth thing".
Why aren't space telescopes put in GEO?
It's a crowded place, and there's a lot of "space citizenship" necessary to stay there. You have to worry very much about station-keeping in order not to drift near any of your ultra-expensive hardware neighbors, and that can interfere with science scheduling.
A communications satellite can do stationkeeping at the same time it serves its primary function because its antennas don't need to be pointed with arc-second stability like an optical telescope would.
It took a lot of work to boost Hubble up to 540 kilometers above much of the atmosphere so that it wouldn't have to do station-keeping burns. Putting it in GEO could actually force it to do more station keeping, exactly opposite of what you want.
The chance that a future big-science optical or radio space telescope for Astronomy will be put in LEO or GEO as the best place for it is very small. These days spacecraft reliability is very high, on-board computing and image processing can sort and pre-process data somewhat, and X-band links even in deep space can do data-dumps during short periods of time. See this answer and this answer.
While MEO could avoid station-keeping that would be necessary in LEO or GEO, I think most telescopes will be much farther from Earth's reflected light and radiated heat, either like TESS which spends most of it's time almost as far from Earth as the Moon, or JWST out near Sun-Earth L2.
The moon is another option. Without any atmosphere so a UV telescope (like those on the Chang'e landers) or IR telescope could work there without needing to be attached to a spacecraft. A radio telescope on the far side would also be shielded from artificial electromagnetic radiation from the Earth, as well as light and heat from the Earth during the two week long lunar night.
There are so many places to put future telescopes, I don't think we'll see any major ones in LEO or GEO. The only reason for GEO would be a low-budget, like a cubesat or nanosatellite project where one uses a low-cost multi-satellite release (see this answer or this question or this question (not everyone can see it, you can also get an idea by looking at this question).