Take many short expo images, and integrate them. This way you will have smaller streaks.

Yes, the sats will occlude things anyway, and their brightness is a big problem, but they are fast moving, they can be mitigated by moving to may short expo images combined. Yes, it's an undue burden, SpaceX should do more, but they can't solve it completely.

The readout time for astronomy CCDs is typically between 2 and 30s (going faster produces more noise), so there is a lower limit on how short you can make exposures.

In LEO the apparent movement of satellites is around 3.6 arcmin per second, which means for an average sized detector that covers maybe 20 arcmin it takes about 6s to produce a streak that covers the full length of the detector (bit longer depending on the angle). If you want it to cover less than 50% of the length of the detector you have to limit your exposure time to under 3s, which means your duty cycle will be between 60% (if you have a fast camera) and 10%(!).

And that's without even considering the loss of sensitivity you incur, because each image will have lower signal to noise since even with those long readout time the readout noise is still significant.

I'm not sure you're thinking about it the right way. Or maybe I'm not. It seems you're assuming that every exposure you take will have a streak in the same spot from a satellite. It's more realistic that a large portion of exposures will have no streak at all, or that if you re-exposed a detector on the same piece of sky, any streak it would see the second time would be in a different place than the first. So if you expose twice and do some basic interpolation to remove the streaks, you would end up with an equivalent zero-satellite image from two exposures.

What am I missing?

The piece that people are missing is the concept of SNR, or signal-to-noise ratio. These streaks are noise, which raises your noise floor and thus raises your detection threshold. Think of the way your eyes adjust to bright light - you can no longer see dim things around it even if they aren't obscured.

Ok, I understand, thanks for clarifying. My next question would be how many exposures would you need in a real-world setting to mitigate the issue? Ex. what's the actual likelihood of a satellite crossing your target piece of sky during a randomly chosen exposure, and how long will it be in the exposure, messing with your SNR?