Do people compete for self-funded studentship? I know that any admission application is subject to review, but I was thinking that the main competitions and open calls are for funding. If someone has full funding and a reasonable resume can directly apply for PhD programs in top universities (MIT or Oxford). In other words, there is no limit in available spots for applicants if self-funded and a supervisor is interested.

I saw some call for applications: for example. UEA is not a bad university, but not a university everyone wishes to study there, then waiting for call for application. I mean, students check if Oxford has an open fellowship to apply, but if you have funding, why you should wait for UEA to announce that they have free place for PhD students?

Even for self-funded students, universities normally support with TA or RA programs, but here it is mentioned that a bench fee should be paid in addition to normal tuition fee. And it is needed to have a degree with honors to apply.

My question is: do really student compete for a PhD position even when they are self-funded?

Do they receive some applications on such calls for self-funded studentship OR it is just a tricky advertisement?
At most reputable schools, self-funding will not exempt you from the admissions process. At the best schools, admission is often completely independent of funding.