As for following your own path, well, that's half the reason to look at past work. I don't want to spend half my life working on something, only to then find out it was done (probably much better) by someone else 60 years ago.
"Those who cannot remember the past are condemned to repeat it"
George Santayana,
The Life of Reason: the Phases of Human Progress, 1905
The thread that inspired this one is proof of that. There is very little that is truly new under the sun.
Personally, I take my cue on this from my study of Art (A level) and Architecture (degree).
Seriously, I cannot begin to imagine setting pen to paper for either without having studied how other people approached similar problems before. You learn from their achievements and also from their mistakes. Over time you build a mental library of what works and what doesn't, which, combined with your own direct experience, informs the development of your own language in the medium; a style, if you like.
Just as in architecture, understanding the different ways that Brunelleschi, Frank Lloyd Wright or Richard Meier use space informs how I might organise a building, understanding how Eugène Atget, Cartier-Bresson or William Eggleston might organise life within a frame helps me make decisions when I'm composing pictures myself. I'll include also the study of painting: there's much to be learned about composition by studying anything from Leonardo's
Last Supper through to Picasso's
Guernica.
It might be that I reject it, but at least I have the option of doing so from a position of knowledge and understanding. Unless I go seek out the stuff that inspires me, I'm a hostage to chance and ignorance.
I also play bass: I pay close attention when I'm listening to Charles Mingus, Paul McCartney, John Entwistle, Tony Levin or Norman Watt-Roy. There's stuff there I can use.
That's the practical and didactic argument for studying other photographers.
Perhaps we live in an age of over-saturation of visual imagery and the easiest way for some people to deal with it is to blinker themselves to what has gone before. I know I can't think that way.
Frankly, though, I love photography. I love looking at great pictures. I love working out what makes them tick just for the pleasure of it. I can spend hours looking at Atget's photos of Paris streets or David Bailey's portraits (every once in a while I need to remind myself how damn good they are). I don't need any excuse.