"My understanding is that most people doing theoretical research in quantum computing don't need to have intuitive explanations for their results, since the calculations work themselves out."

I don't believe this. Maybe your classical intuition is wrong, but that doesn't mean you can't develop a quantum intuition. Quantum theory is just a natural generalization of probability theory (with "list of probabilities adding to one" replaced by "list of amplitudes whose squares add to one"), so particularly for anyone who thinks much about randomized algorithms the intuition is very similar.