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I just realized that was very poorly worded. I meant that the buyers agent should always be there or find a co-worker who can fill in for them. It does slow things down if the sellers agent is there. Just out of curiosity why are you looking at Q&A in New Jersey when your in Arizona? Unless you practiced real estate here in the past you don't know how things are done here. It is definitely wrong for the buyer's agent to not be present at the home inspection.
It's rare for a listing agent to be there, at least in the vast majority of locales of which I'm aware ... in fact, it generally slows down the proceedings greatly when either the listing agent or the seller is present as more often than not, intentionally or not, they end up shadowing the inspector the entire time.
As for having buyers there when the agent's not there, it's a little unusual but not necessarily wrong.
Usually the owners are not present at the inspection anyway, so that the inspector can work freely and the buyers can ask questions and make comments freely. The buyers agent is usually there with their buyers, first as a courtesy, and second to get an idea if there is something that will need attention during the inspection phase.
Sometimes there is just a conflict with the agents time, and as long as the buyers and the LICENSED inspector are there, it's not illegal or unethical.
I personally attend all of my buyers inspections. But this is more for the benefit of the buyers as opposed to any security issue as the buyers don't have access to the lock box.