Re: Twinkle, twinkle.
They're called ephemeride tables, and they're published, free of charge, by the satellite operators and various spacewatch organisations. So that just leaves planning observations around not pointing where a satellite will be illuminated by sunlight, or briefly shuttering the sensor as one passes by. This is easily within the capabilities of modern telescope pointing software.
I think you'll find that the idea predates Musk by a decade or five. Remember Iridium? Musk is simply the first to have the wherewithal to do it economically.
Something else to consider, the cheap launch capacity that makes Starlink possible also means that we could easily launch half a dozen or so Hubble class (perhaps even better) instruments into orbit for about the same price as the original Hubble mission.