People earning an equivalent of a couple USD a day, or nothing at all, aren't going to be able to afford to pay some US corporation for fast internet.
Fast internet probably isn't even a concern in wartorn countries, honestly.
Let's be honest - Starlink is almost exclusively going to be used by people living in rural areas within developed nations.
Why would the US Government (aka. Taxpayers) pay for internet use in other nations?
We already have expensive problems domestically that people would rather spend that coin on.
You drop access to the internet as whole in places where the internet is suppressed or non-existent and the populace learns just how bad they have things then they might revolt on their own.
I wouldn't say I 100% advocate for the idea but thats the thought process behind it.
You would also have to deal with the real possibility that those countries would simply shoot down any planes observed dropping Starlink base stations.
The Human Rights Foundation even collects flash drives to load them up with content to smuggle into North Korea: https://flashdrivesforfreedom.org
For a government to do this? How could that not lead to an armed conflict?
You're not wrong, information/propaganda warfare is aggressive. Sometimes it makes more strategic sense then open warfare, and sometimes states can get away with it when they can't get away with open warfare.
I would very much like to see a headline of a neutral nation airdropping supplies into a country engaged in war without getting dragged into the conflict. I'm not aware of that having occurred in the past 4 decades.
We don't drop satellite modems into war torn countries now, and we're not going to start doing that just because Elon Musk needs to check off one of his PR claims.
And at $2000/pop, they're at least as expensive as the equipment we're currently not randomly dropping around the globe because of the expense.