Can a defendant voluntarily relinquish his probation? If so, what statute or case law allows this? (In other words, saying we do this all the time will not suffice in this case).

Check out 42.12(5)(a), the last sentence:

"[U]pon written motion of the defendant requesting final adjudication filed within 30 days after entering such plea and the deferment of adjudictation, the judge shall proceed to final adjudication as in all other cases."