They will have to turn it off over countries that don't fancy free communication and are capable to get a projectile in LEO or have a market for electric cars.
It is probably cheaper to launch a StarLink bird than it is to blow it out of orbit. Think of it as a DoS attack on the launch batteries!
As for the second? I find that approach much more likely to succeed. Sigh.
They have some propellant to make adjustments and stay in orbit a bit longer but if you blow them up you just make the decay process quicker.
First, it's one of extremely few actions actually likely to get you nuked or "liberated" - you just threatened one of the most valuable strategic advantages (even if it's just a civilian satellite, it wasn't yours, and militaries will consider their satellites under threat).
Second, in case you're not aware, the remains of the satellite now are a danger to any other object in that orbital plane, and this can trigger a cascade reaction and take lots of them down, making new launches impossible for many years. Look for Kessler Syndrome.
Nobody is nuking anybody else over satellites. Nukes will only be used in case of regime / home territory threat (eg if Russia were losing a conventional war, and NATO were pushing toward Moscow, Russia could throw down the nuke threat card and say stop or else), or in response to the use of a nuke.
If North Korea starts shooting down US satellites at some point, it would prompt a conventional military bombing response (which would attempt to neutralize their ability to launch rockets at US satellites), and possible full-scale war. It would not prompt a nuclear retaliation. There is zero interest - anywhere - in seeing millions of people die over some satellites.
The plan for Starlink is to have 12,000 satellites eventually. You'd need to shoot down quite lot a of them to block access to an entire country.