> I would be very suspicious that they will burden me with all kind of side activities (e.g. tutoring undergraduate students, handling bureaucracy, paper work, etc.) that are not really of any actual help towards the thesis.
What you're calling a "burden" is the stuff that (a) pays for the funding that covers tuition and living expenses and (b) provides experience that helps you to get a job when you're done. You don't need to burden yourself with those things if you pay everything yourself.
In my experience, some universities/programs still expect these ancillary duties even if you're self-funded. If I was a cynic, it would lead me to believe they are just trying to get cheap labor out of grad students.
Both of your examples are duties that an academic may have in the future. What about someone like the OP that just wants the PhD and continue their path in the industry?
Speaking anecdotally: the US research universities seem like research mills driven by low wage labor from international students. American students I met in my graduate program had to be both really smart or passionate and willing to put up with the demands of the PhD. It’s pretty bleak, and it’s good to hear that it’s different on the old continent.
What you're calling a "burden" is the stuff that (a) pays for the funding that covers tuition and living expenses and (b) provides experience that helps you to get a job when you're done. You don't need to burden yourself with those things if you pay everything yourself.