The Elon aspect has already been covered by other commenters, so purely against Starlink's technology as a primary method for internet, ignoring Musk:

It has an enormous carbon footprint. Launching stuff into space takes a ton of energy, and SpaceX rockets are entirely powered by fossil fuels. Most of the rocket body is just massive tanks of fossil fuels, and because they don't fly very far from Earth, most of that ends up in the atmosphere. The internet already has a significant carbon footprint, and adding this layer when we absolutely don't have to is stupid. We can build A LOT of terrestrial radio infrastructure for less environmental impact, covering pretty much all rural areas. Microwave dishes pointing to towers is superior for rural internet in pretty much every way, including latency which is Starlink's main selling point over older satellite internet systems, and wired internet is still the best option in every benchmark possible so using Starlink in urban places where you can effectively supply wired internet is stupid.

But what about people who live in super remote areas where ground based infrastructure is unfeasible? Well, we've already had internet capable satellites for much longer, and Starlink is an inferior satellite technology in terms of efficiency compared to satellites that orbit much higher up. They fly so low that most of the time they're doing nothing because they're flying over the ocean or places no one is using the service. With geostationary satellites, each satellite can "see" a larger portion of the Earth, so not only do you need fewer satellites while still providing global coverage, each satellite is in use much more of the time even when they're flying over unpopulated areas because they cover so much more area, so say, ships and wildlife researchers in the jungle can stay connected to a single satellite instead of needing a dense web of satellites flying by overhead to deliver continuous coverage.

Flying so low also causes them to experience much more atmospheric drag, meaning they have a much shorter life. So you need more launches in total to replace satellites and maintain global coverage, massively increasing the carbon footprint. You also further pollute the atmosphere with vaporized satellites (which contain some nasty heavy metals BTW) when they run out of propellant and fall back to Earth. So not only do you need fewer satellites with geostationary orbit, each satellite also has a longer life.

The antenna you'd need on the ground is also much simpler, just a dish instead of an expensive, fragile, and power hungry phased array. Pretty important for truly off grid people.

It's also bad for national security (again, speaking on national security implications of the technology in general because as a Canadian I couldn't care less about US national security) to rely on it as a primary way of getting Internet because, as we've just learned, other countries can just shoot down your satellites when they fly over their territory. Not helped by the fact that they're so close to the ground. It would be a lot harder to attack infrastructure in a country's own territory. And if you're not the country operating it, you're also at the mercy of that country because they can just deny you access.