All motion in space is relative. Whizzing by what? A rocket goes straight up.... sort of. Maybe. If you look at it from the right angle. You can plot the motion, as they already do for existing stuff. I don't think it's the biggest issue in the world. Bear in mind SpaceX are making money off rocket launches. I doubt they're going to sabotage their own business and I also doubt that they'd have been licenced if they were as bad as you suggest.
As for astronomy, don't I know it. The things are a pain. I've already seen a few of them. Seeing satellites isn't anything new and neither is working around them with a telescope as they tend to move out of the way briskly. Astrophotography packages normally have ways of automatically getting rid of them. But, there are going to be thousands of these things rather than old school global comms systems. As an example, GPS has only 31 in orbit and current, operational bidirectional sat comms systems tend to have tens of them. Boeing is also planning on putting a couple of thousand satellites up there and there are other systems being planned.
Maybe I'll buy myself a ground station, hack them (because that'll be so easy) and see if there's an emergency "BURN_UP_ALL.exe" file I can run? The meteor showers have been a bit disappointing of late.