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.
Interesting, although the existence of this research actually suggests that normal Bayesian opt by itself is not safe and needs to be modified to be so.
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.
Indeed -- safety in exploration is not a relevant concern in all (or even in most) scenarios. However, in domains such as robotics where certain configurations may have unforeseen and severe consequences, you may want to slow down exploration and proceed more cautiously. As you suggest, you can optimize more efficiently if you can explore the domain without any safety concerns.
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.
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.