I think it depends whether you can leverage some knowledge. It's possible for a person/LLM to look at a loss curve and say "oh that's undertraining, let's bump the lr" - whereas a Bayesian method doesn't necessarily have deeper understanding, so it'll waste a lot of time exploring the search space on poor options.
If you're resource unconstrained then BO should ofc do very well though.
Yah, I'm a bit skeptical - ime humans tend to under explore due to incorrect assumptions. Often this is due to forming a narrative to explain some result, and then over attaching to it. Also, agents aren't actually good at reasoning yet.
Good Bayesian exploration is much, much better than grid search, and does indeed learn to avoid low value regions of the parameter space. If we're talking about five minute experiments (as in the blog post), Bayesian optimization should chew through the task no problem.