- There is only one clear path and no chance of getting lost;
- The floor is course sand that won't silt even with a group of divers swimming through the cavern;
- It is so spacious that many divers can pass through at the same time;
- The cavern has multiple large entries and exits; and
- It is well illuminated.
You've eliminated many risks of overhead diving in your assumptions. If you can't silt out the viz, and you can't get lost, and there are lots of places to get out, and you could easily share gas with another diver, then the remaining factor of overhead diving is simply that you can't panic and bolt. The Ginnie Ballroom meets many of your criteria, apart from multiple exits and light, but a woman died there because she got stuck to the ceiling and couldn't sort her buoyancy out to leave the cavern. I believe she drowned with gas in her tank.
You will read many discussions of diving risks, and some of them are what a good friend of mine calls Little House on the Prairie scenarios. I never watched the show, but apparently every episode would involve situations where many implausible things went wrong. Any of us can posit a situation where so many failures occur that the dive is not salvageable, but those situations are (thank God) not often seen in reality.
If you are swimming through a huge, well-lit space like the Cathedrals, that you can't silt out and you can't get lost in, it's highly unlikely anything bad will happen unless someone has a problem and panics. Panic kills in diving, but it particularly kills in overhead environments.
Most of us who have a fair bit of diving experience are going to be able to cope with a flooded mask, or a freeflowing regulator, or a lost fin, or some other fairly normal malfunction, without deciding that the only option is a direct and frantic bolt for the surface. We are unlikely to get into trouble in the Cathedrals, or swimming through the aft section of the Rhone. But I have read a hair-raising account of a man whose wife almost died in Devil's Throat, by mistaking a crack that admitted light for a route to the surface, and getting stuck, and panicking. So even in well-lit and reasonably commodious swim-throughs, risks remain, especially at significant depth.
Did I do swim-throughs before I had overhead training? Yes, I did. Did I consider each situation carefully, knowing that overhead environments are in general inadvisable? Yes, I did. Did I get in any trouble? No. Do I think the likelihood of trouble was high? No. The problem with taking those examples and running with them, though, is the slippery slope concept. If it's okay to swim the Cathedrals, is it okay to swim the cavern at Hole in the Wall in Florida? A family of three almost lost one of their members by answering that question in the affirmative.
I think overheads, even simple ones, up the ante on the risk of the dive. They are appropriate for experienced divers who have some familiarity with their reaction to stress or malfunction. They should be chosen carefully to meet the criteria listed in the original post. And they should not lie at depths where narcosis is a major factor.