Except that several of them were...

There was Rory Williams as the main standout, but Martha Jones was working as a nurse when she joined the show. She was still at the end of Med School, and it was a (very minor) plot point at one point when she earned her doctorate.

Strax also counts, Well, he did until the Doctor screwed up and got him killed. The resurrected Strax was not much of a nurse.

There were a few more who were outright medical doctors when they joined the show. One was a British Navy surgeon, and the one that might not count, the cardiologist from the Doctor Who movie, which most people sort of ignore.