When I began to play the accordion, I spent a lot of time "parroting" the masters, at least as best as I could.
This was in the early 90's, and I greatly admired the playing of Marc Savoy, Steve Riley, Jimmy Breaux and others who were actively recording and playing at the time. I also learned about the greats from earlier years: Nathan Abshire, etc.
I learned a large number of Cajun songs and could play them in varying degrees of OK-ness. I still think that parroting is important, but looking back, I can see that I slowed my progress by parroting the best of the best. I mean, Riley, Savoy, Breaux, etc. - these guys are the world class virtuoso players of our time. They are in a class of their own. Additionally, they built on the styles of the earlier players and expanded the frontiers of what could be done on the accordion. I think I would have been better off going back to the players of an earlier time and focusing more on that. Actually I did do that to some extent, but I think I had overly ambitious goals of playing at the same standard as the modern virtuosos. And in the end, when playing at gigs, my versions of the Cajun songs I played were greatly simplified compared to the masters. For practical reasons, it simply had to be that way.
The other thing I want to say is that if we keep at it long enough, our own style will eventually emerge. We are not the same as those we emulate. Our personalities and experiences are different, and no matter how hard we might try to copy others, inevitably it will not be the same. It will just happen on its own. That is how it should be.