I broadly agree with you, but I'm wondering if you would reconsider your qualification as "less complicated" if you consider beginner learners. E.g. someone who knows basic descriptive statistics and probability theory, and is making first contact with inferential statistics. Specifically, assume a learner who knows what an integral is, but is far from proficient with it (UGRAD student, not a GRAD student).
I was reading this paper[1] recently, which highlights two difficulties of teaching Bayesian stats: 1) the mathematical complexity of understanding conditional probability distributions, and 2) the lack of well defined, broadly accepted conventions for what priors to use in specific data analysis scenarios.
I think a computational approach to prob theory could mitigate 1), but 2) remains a problem—the freedom to choose priors, is also a burden...
[1] https://www.stat.purdue.edu/~dsmoore/articles/BayesPedagogy....