Their weakness come through when you realize that all these exact calculations, are based on data that isn't. A winds aloft forecast will never be accurate in either direction or velocity. An experienced pilot's best estimation is just as useful as what you'd come up with, spinning the whizz-wheel. And if you ever planned a flight where being exactly accurate was crucial, you're pushing limits like fuel duration WELL past "my" safety margin.
I 100% agree. Your calculations are only a rough estimate, so solving something like airspeed to a tenth of a knot doesn't buy you anything.
I am also a fan of the whiz-wheel. I bought an electronic E6B a long time ago, it's still in my flight bag but the batteries have been dead for years. Simple math like multiplication and division may be faster on a calculator. But for flight planning, because the calculations are repetitive and don't need to be exact, I think that I can actually do it faster (or at least no slower) on a wheel.
As Brett put so well, I'd stick with the wheel until you've mastered it, as it will give you a much deeper understanding of how all the pieces fit together. After that, it's a matter of personal preference. If you like pilotage, dead reckoning, and sectionals, you'd probably prefer the wheel. If you like GPS and autopilot, you'd probably prefer the electronic E6B.