Satellites already cause problems for telescopes, but not by obstructing their view. Actually the light reflected from satellites is a bigger problem, and for observations of radio waves, their communications are the really big problem.
In terms of reflected light, you might remember the controversy around the "Humanity Star" being too bright. The same applies to starlink, which this image shows really well:
Credit: CTIO/NOIRLab/NSF/AURA/DECam DELVE Survey
Radio wave observations are important because they allow astronomers to look the furthest back in time towards the big bang, when everything was strongly red-shifted. They are also used for measuring pulsars, and for SETI. Satellites only use discrete frequencies for communications (broadened by doppler shifting) but there are already so many communications, and signal strength is so much stronger than what we receive from distant galaxies that removing the noise is a topic of active research. Due to the long wavelengths, radio wave antennae have to be quite large, so these telescopes are usually earth based - there are not many radio wave telescopes "above" LEO orbit which would give us an untainted view.
While researching this, I read that variations in the brightness of a star are important for detecting exoplanets, and satellites blocking that light momentarily could disturb the measurement. I would have expected that the timescales for the satellite and the planet to be blocking the light would be different enough that you could filter that out - but it would be an additional noise source for what is already a very sensitive measurement.