Having taught frequentist stats as a TA to grad students, I understand why frequentist stats seems not to make sense. On the other had, my prior on teaching quality, and my data on the relative difficulty of understanding the approaches says with near-certainty that your experience has nothing to do with the approach taken.

Having used Bayesian stats heavily, I'd note that the hard parts are not gone, they are just located elsewhere - in how to actually do the computations, rather than in how to set up problems. Each can be taught poorly or well, but given that MCMC is certainly harder than least-squares, it seems difficult to argue that using Bayesian statistics is easier. (Unless you're not just applying the methods by rote, and letting the computer spit out answers - and if you are, I don't know why you are better off with Bayesian methods. In fact, if that's what you're doing, please stop doing statistics and pay an expert instead.)