I don't understand why you would say that. Tiger was not and is not the most influential golfer ever. In fact when it comes to style, I'd say he has had a somewhat negative influence. And, he was a coddled child literally bred to play golf; that's not something that golfers can aspire to. So, I'm not sure what you mean by "influential."
Vardon was the early innovator and introduced the grip that most people still use. Jones was a major celebrity and elevated the game worldwide, demonstrated utmost integrity, gave true meaning to "play for the love of the game", as well as being a pioneer in instructional video and an excellent writer, to boot. Hagen innovated wedge bounce. Hogan's swing is more influential than Tigers, to this day. Player introduced working out and nutrition. Palmer was a celebrity-media pioneer. ...
I wouldn't say there are 'pitfalls' necessarily. What is common knowledge here is this: There are 5 keys necessary to have an efficient and productive golf swing.
1. Steady Head 2. Weight forward 3. inline impact 4. Diagonal Sweetspot 5. Clubface control.
How one achieves these keys can obviously be quite different. If you can achieve these keys with your 'single plane' swing so be it. But I would focus more on these keys rather than this 'single plane' idea.