I'm not completely sure, but I think the lack of exploration in your small example may be a kind of "model overconfidence". The model believes that there is less chance of improvement far from 1 than there may actually be. This may occur because the GP fitting algorithm uses a point estimate for the GP kernel parameters, rather than integrating over the predictions of the model using the full distribution over kernel parameters. In Snoek's paper for example, (see bottom of this page), they advocate integrating over the kernel parameter posterior, but we don't do that, mainly for speed reasons. Integrating would probably make distant regions more uncertain.
Another factor here is that our GP modeling function, fitrgp, does not allow the noise variance to be exactly zero. So we approximate the noise-free case by using a tiny but positive constant value of Sigma. That is why the model still thinks there is a nonzero probability of improvement at X=1.
Finally, in order to avoid overexploitation, we use a version of Bull's method (see reference on same page). This temporarily increases the global kernel amplitude parameter, which is one way to make distant points look more uncertain. It does this a maximum of 5 times until it finds a different "best" point. After 5 tries, it uses the best point. For noisy problems, that has the effect of decreasing the uncertainty at that point, and so eventually it will look elsewhere on future iterations. But in your deterministic case, the tiny variance can't decrease any more.
In your small example, bayesopt is finding the right answer. In your real problem, I assume it is not. Judging from your acquisition function plot, bayesopt seems to be estimating a tiny kernel scale for your problem. Is your problem really deterministic? If so, if it's a highly variable function, you may get better results by telling bayesopt that it's nondeterministic.
