Absolutely, in fact it's pretty easy and is routinely done by amateur and professional astronomers alike. We've had satellites, airplanes, and meteors obstructing astronomical images ever since we began taking them.

A very simple and common way is to stack all of the static images aligned on top of each other such that you have a set of values for each pixel corresponding to the same region of sky. Then sort the values of each pixel by brightness and keep the median value for that pixel. Or throw out that top and bottom 10% and average the rest, or throw out the top and bottom N, etc.

This is a standard feature of essentially all astronomical image processing software and has been for a long time.

Sure. But increasing the number of frames with tracks increased the number of datapoints you need to throw away, reducing the effective time on target and therefore sensitivity of your observations. Astronomers are not idiots. They know how to deal with obstructions. But that is not free of cost. Neither in observational limits nor computer time nor required brain power.

Sure it's not without cost, but in most cases the cost is not very high.

Remember you don't need to throw away the whole frame, only the pixels that were obstructed. One track across a frame will obstruct less than 1% of the data in that frame.

One of the key assumptions that's being made, throughout this thread, is that astronomy is mostly imaging. Taking or stacking images. A ton of astronomy is spectroscopy, which is nothing like a stack of static images with one that has a streak in it.