So if you're a Bayesian decision-maker, doesn't that mean that you only ever face decisions under risk, because at they very least you're assigning ignorance priors to the outcomes for which you're not sure how to assign probabilities?

Correct. A Bayesian always has a probability distribution over possible states of the world, and so cannot face a decision under ignorance as you define it. Coming up with good priors is hard, but to be a Bayesian, you need a prior.