Being a doctor is his raison d'etre. Sure, the Doctor likes his opera, he enjoys pulling a Pygmalion on Seven of Nine every now and again, but he's really defined by his profession since being a doctor is, literally, what he was created to do.
Is he always great at it? Uh... no. But here's the thing -- he's dealing with stuff week-to-week that virtually no Starfleet doctor ever has before. And the Doctor is having to build skills off of his somewhat limited software.
So, yeah, sometimes he turns into an evil version of himself on accident. These things happen. Yes, his attempt to be a therapist caused him to convince Seven she was Borg raped when, oopsie daisy, she wasn't. And sure, sure, there was that one time he failed to prevent Paris and Janeway from mutating into intergalactic platypi and breeding together, but that's all water under the bridge!
The guy is supposed to be an emergencies only stand-in. He's the Bat Phone, not the "darn, I stubbed my toe" phone! But I challenge you to find any doctor more dedicated towards self-improvement. The Doctor leaves the ship frequently to visit other worlds with the specific intent of attending medical symposiums. And, even though it sometimes yields unexpected results, the Doctor does rewrite his own program with the specific intent of being better at what he does.
But if all those generic platitudes do not persuade, you, let's get real and consider "Latent Image," an episode that defined the Doctor in a way that perhaps no other Star Trek doctor has ever been defined before. In it, he discovers that his memory has been erased to remove an instance where, given the equal choice of saving one crewmate over another, he chose to save the one he knew best. His program breaks down because of a flaw -- it cannot explain why he would choose one person over another, it cannot condone that he might have unethically played favorites in the realm of life and death. But the Doctor unlocks those memories and, rather than having his mind wiped again, sits in the holodeck, largely by himself, to learn how to live with the impossible decision he had to make.
Basically, if I was sick with anything except Space Platypus Disorder (it's a serious affliction, y'all), this is the doctor I'd see.