Some research has explicitly considered the question of safety during exploration; see for example https://arxiv.org/pdf/1602.04450.pdf which includes theoretical analysis of the resulting algorithm.
A relatively unique trait of Bayesian opt is the modelling of unexplored space. The attraction to exploring that space makes it actually less safe than other methods that do not explicitly care.
One could go through similar steps to model and generate safe steps in other methods. It doesn't seem specific to Bayesian opt. It might even be better since it's less likely to be so computationally expensive as the auxiliary opt within Bayesian opt tends to be.
You're correct that the approach taken in the linked paper could be adapted to increase the safety of other sequential design settings (when needed), assuming you have access to a model that can quantify uncertainty.