I agree with you about more gadgetry the more chance of failure...I think that's covered in Chapter 8 of the KISS manual. ;)
The router control that seems to work well is a cheap one that costs US$20.00 or less if it's on sale. The guys talking about them seem very satisfied with them. I'm thinking the plane runs 500-600 watts and these controllers are rated at up around 1800 watts.
Anyhow... I haven't used a knife, but watched an old fellow down close to the Florida line (O.J. Blount) use a *cold* knife to uncap two supers. He believe he did have a heated pot he kept it in when he laid it down. It really seemed to work ok for him. The uncapping plane can he used to touch up the comb...tilting it to the side at a slight angle lets you use one end or the other to some extent. It is really good, too, for cleaning up the edges of the frames. All along I still used the scratching fork to take care of skipped (low) cells.
It would seem, for deep frames, that a knife might be a touch better in that you would have one smooth surface on the comb once you made a pass with it. With the plane two passes would be required and the overlapping edges may or may not be flush with one another. I'll have to let someone else give you some actual feedback on using the plane with deep frames, though.
I'm trying to decide on several items for my "honey house" so that I can have it delivered this October at our state's annual beekeeping meeting (no freight charges). Knife or plane is a deciding point for me, too.