Some may go for it, but as a career troubleshooter (48 years) in electronics I would never do it.
Suppose the mechanic checks your car and, as a result of a visual inspection, finds your car has a bad head gasket. You pay him for his time and shop materials, buy a head gasket and a Chilton's manual, and set to work. You may be doing good work with professional standards, but then you probably would have been able to diagnose it yourself. You may lack some niceties, like a torque wrench, but figure you can just tighten that sucker down. It isn't like the bolts stretched the last time they were installed, is it? Okay, a professional would check the surfaces to see if they are really flat, but they look okay. You reassemble it and it runs... but the next day it is low on coolant and it overheats after half an hour. All that work for nothing! And that is even if he didn't miss the diagnosis... that happens, too.
Who do you blame? It sounds like a bad diagnosis to me. That mechanic didn't know what he was doing! That may sound far fetched, but I was alerted to help out a neighbor in Phoenix who had a dead home A/C. When I arrived he was finishing up a phone conversation and was saying, "I just want to know where to pour the freon in!" He hung up the phone in disgust and complained, "That guy didn't even know what he was talking about!" My neighbor had a can of R12 and a beer can opener in his hand. Needless to say, the unit did not need freon, either.
Mechanics like to supply parts because it is a clean decision how to handle it if the part is a dud and the labor is significant to replace it again. They also like to keep their diagnosis and repair together for pretty much the same reason. It is just a smarter way to do business.