Wrong in your first statement, so wrong in your second. A plane, depending on style, can do a great many things beyond fixing problems or errors. In many cases, a good rabbeting plane is the absolute fastest and easiest way to form rabbets. Smoothing some woods is far easier with a good plane than with any other tool. At one time, making molding was the province of planes. It still can be, and is especially useful on small jobs where setting up for power molding cutting is a hassle. You're done with the job using planes before you can even finish bolting down the shaper cutters, or before you can even find the right router bit.
A plane is one helluva lot more than a tool to fix mistakes.
While I'm not much on mysticism of any sort, you might want to borrow and use a couple of good planes to make a small box or bookcase, to gain a feel for the wood that you cannot gain with power tools. That's not mysticism, though, it's simply removing one layer between you and the natural material.
Charlie Self
"I think there is a world market for maybe five computers." Thomas J. Watson