I understand the goal is not pretty pictures. But you're not using a hammer to remove random white noise from all your observations, you're using a scalpel to mask out completely predictable errors for very short periods of time. My amateur astronomer link was not meant as a scientific how-to, but as an illustration that even simple hammer-y methods work to mask out satellite trails.
There are very few non-periodic events in the universe that happen over the fraction-of-a-second timescale for which a satellite occludes an area of the sky, the linking of EM to gravitational wave events being perhaps the only notable exception. Meteor impacts on planets happen over the course of seconds. Supernovae occur over the timeframe of hours. Glitches in millisecond pulsars (the millisecond name notwithstanding) occur over the timescale of days.
This is also the issue with using occlusion by the sun and moon as analogy - their occlusions do operate on the timescale of interesting astronomical events. If the moon whipped around the Earth at the same rate as LEO satellites it might occlude Jupiter, but you would have plenty of vision between the shutters to reconstruct events on the timescales we are interested in. I'll also note that the analogy breaks down with the focus on objects in the solar system since they all roughly lie on the ecliptic - you've reduced the occlusions over a 2D sky to occlusions between objects that live on a 1D slice of it. The Sun and Moon both take up 0.3% of the angular diameter of the sky, but only 0.001% the angular area.
Are you losing real data with a sky full of 10's of thousands of LEO satellites? Yes. Is it a significant amount? Not by any reasonable metric. Is it over a significant timescale? No.
An analogy: If you have some video footage and for whatever reason have a punchhole in the corner of every 100th frame, that by no means precludes you from doing analysis on the video. I'd expect the video conservationists to be up in arms about any blemishes on their original film, but I'd argue that that is the position from aesthetics. To answer questions such as "how many times does the ball in this video bounce" or "how does the lighting in this video change over time" or "how does that person's hair react to the wind visible in the video" the hole is insignificant to obtaining the answer, even if the area of interest is directly covered every 100th frame.
I'll close with the acknowledgement that radio interference is a legitimate concern here. But satellites are hardly the only emitters which are increasing in number at an increasing rate, and that commons will be polluted whether we launch them or not.