It is not like simpler voting methods are without subtleties (and I certainly wouldn't call electoral college simple!), but these subtleties are well-known and everybody is kind of accustomed to them. Again, immediately abandoning ordinary voting and switching to QV on the level of countries would be stupid, but I don't think they are advocating that.
> Hell, I know a fair bit of math and CS, and I would feel uncomfortable quickly deciding how to divide my votes across issues, let alone advising other people on what to do.
This can probably be less of a problem with sufficiently good UI. Imagine that you can play with some sliders and immediately see the consequences of your actions. After some fiddling you will probably get pretty close to what you want. Some friction can even be beneficial, encouraging people to be more thoughtful about issues. There was a study (link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2755844) where they used QV in opinion polls and were able to get more information about relative preferences of participants because they were forced to think about correctly allocating their credits instead of blindly answering "strongly agree"/"strongly disagree" even if they didn't really care about a particular issue.