I am told, by both a professor at my US undergraduate school and here at Stack Academia (for example, at Implications of being accepted without funding to a computer science PhD in the United States?), that I should not accept an offer from a US graduate school unless I am offered full funding. The reasoning is that if they actually wanted me, they would be paying me. I agree with this.

So my question is, what would be the difference between going to a school with funding and without funding, besides the money? Would I be treated as a second class citizen? And if I was offered full funding, perhaps from a TAship, what would happen if I wanted to pay for myself anyway?

Existing answers, such as at Will self funding a PhD hurt employment chances?, seem to focus on the money and the chance that the applicant is not strong enough for the program. While I also agree with these, I am interested in learning about external factors too.

I am told, by both a professor at my US undergraduate school and here at Stack Academia (for example, at Implications of being accepted without funding to a computer science PhD in the United States?), that I should not accept an offer from a US graduate school unless I am offered full funding. The reasoning is that if they actually wanted me, they would be paying me. I agree with this.

So my question is, what would be the difference between going to a school with funding and without funding, besides the money? Would I be treated as a second class citizen? And if I was offered full funding, perhaps from a TAship, what would happen if I wanted to pay for myself anyway?

Existing answers, such as at Will self funding a PhD hurt employment chances?, seem to focus on the money and the chance that the applicant is not strong enough for the program. While I also agree with these, I am interested in learning about external factors too.