What are the benefits of fully discrete amplifiers as opposed to op-amps?
As a blanket statement, none. A specific discrete design can be better than a specific IC, and vice versa, for a specific application.
The proper question to ask is, when is one design approach better than the other? What are the strengths and weaknesses of each?
Starting with discretes, an obvious advantage is the possibility to build something with properties not available in an IC. Now there are a staggering number of different ICs to choose from, so in practice just about anything imaginable does exist. Certainly for audio applications, it is rare to have requirements so unique that an off-the-shelf IC cannot be found to do the job.
Finding advantages for ICs is not difficult. Their small size means more elaborate circuits are feasible, should this be of benefit. The manufacturing process inherently gives much better matching of components than is (easily) possible with discretes. Moreover, in an IC each transistor can be tailored to its function, while with discrete parts the designer is stuck with whatever is available to buy.
Ultimately, of course, what matters is how well the finished product performs and at what cost. Both approaches can deliver vanishingly low noise and distortion, so the choice will have to be determined by other factors.