My taxes aren't "money given without strings attached". They are payment for services that benefit myself and others in the community. They're not a free gift for the government to hand out, that's theft.
No, student loans are not slavery for two reasons. First, the borrower agreed and signed a contract. Second, the debt owner is the one calling it due.
This is substantially different than expecting control on how debt free doctors or engineers spend their time or what jobs they work.
The crux of this is that externalty price analysis is only useful when bounded by real harms and property rights. Otherwise, anyone can call anything they dont like an externality: If my employee quits for a better job- Externality! If a woman wants to go home to their family instead of having sex with me - Externality!
I believe that’s how it is in some places. In others, there’s no obligation after receiving a subsidized education, and this would be a way to fix that. I doubt many people would propose or defend a system where graduates are required to work for the state or go to prison.
It might be evidence that you or your government isn't benefiting you with its spending. That doesnt put obligation on the recipient.