I'd actually go beyond what you've just said. If the qualification means anything (and that is a leading question) the dive should only be attempted by (in PADI terms) current divers holding the deep specialty. Even so the dive is still deeper, as the Deep specialty takes you to 130ft, and the shelf people dive to reach or at least to see is at 150ft.
I was once a "passenger" on a BH dive run by another dive operation, on which I noted that many of the divers were using rental equipment that didn't have a depth gauge, and even the lead divemaster had only a depth gauge and not a computer. I was wearing two computers and both went fairly well into deco, maxing at 8 minutes before we started to ascend. One of my computers had cleared when everyone was already back on the boat but the other (a Suunto!!) hadn't, so I decided to bend it in the interests of harmony. It was beeping loudly when I climbed the ladder, and the captain took me to one side to tell me that I was setting a bad example to the other divers. My reply was that the whole dive as conducted was a bad example to all the divers, and all my computer was doing was telling them what they should have known anyway but the crew had omitted to tell them. Or something to that effect! Especially remembering that some divers, all of who had dived the same profile as I had, had been back on deck for 10 minutes when I boarded. Isn't ignorance bliss!
As to accidents, there have been deaths in the BH on these "standard recreational dives". Not recently so far as I know, but certainly in the last few years.
My view is that there's no excuse taking people on a dive they are so unsuited for that they don't even understand the issues they face or know the dangers.