This may be one of the shortest "Swing Thoughts" ever posted, because the point I'm going to make is very simple.
Unless we're literally talking about Iron Byron (the machine), everyone is a feel player.
I've yet to meet a golfer who has mechanical dials and switches so that I can program him to "rotate his left forearm 27.5° by this particular point in the backswing." Rather, two golfers with identical swings may feel like they rotate their forearms a completely different amount, including the possibility that one golfer may feel like he's actually counter-rotating his forearm.
Feels produce mechanics in ALL players.
Too often, someone who is AWARE of mechanics, or seeking to change or improve their mechanics, thinks of themselves as a mechanical player, or is seen as one by other players. For example, saying something like "At A4 I want my shaft to be here, and my lead wrist to look like this." But to actually produce that picture, or those mechanics, the golfer needs to feel something. That feeling will often change throughout time as what was once new becomes standard, or even over-done, and their feelings are unique to themselves - they're not exactly the same as someone else's feelings to produce the same mechanics.
Consider the case of Nick Faldo. He spent two or three years rebuilding his swing with David Leadbetter. He was called "a robot," and while that bled into the kind of player others saw him as, it was more for his consistent play and lack of on-course personality. If you discussed the golf swing with Nick Faldo, he'll talk about feels. He'll say "if I did this, the clubface was square here" or something like that. FEEL produced the mechanics Nick Faldo (or David Leadbetter) knew he needed.
An opposite example could be Bubba Watson. He supposedly doesn't know much at all about the mechanics, and just "feels" the shot he's trying to hit. However, you don't have to be a golf savant to notice that his "big huge cut" swing is mechanically very different than his "big huge draw" swing. Feels produce mechanics in Bubba Watson just as much as they do in Nick Faldo.
So, more often than not, someone who is seen as "mechanical" is simply someone who understands the mechanics of the golf swing better than others. There's no shame in that; in fact, it's a good thing. Imagine if Bubba and Nick, in their primes, have equal levels of talent and work ethic. When Bubba starts struggling, all he has is a list of "well, this feel worked in the past…" while Nick can take a look at his swing, notice what mechanics are off, and then devise feels to correct them while monitoring the mechanics.
But again, how does Nick change the mechanics? Feel.
Every golfer is a feel player. It's the only capacity we have to change the golf swing or produce the desired mechanics. We aren't built with springs, dials, knobs, meters, and so on. Feel is all we've got.