"
A crotch strap" is NOT an anti-submarine belt!!!!!!!
If used that way, you won't care about the damage that might have been done if you slid under the lap belt without it. The ENTIRE point of a crotch belt in a 5-point belt set is to keep the shoulder straps form pulling the lap belt up into your belly. NASCAR started requiring crotch belts, changing 4-point to 5-point belts after the death of Fireball Roberts. He was killed by internal injuries from his lap belt slipping up into his belly."
Remember I am not that young and I have been calling it that long before the (proper) change or terms came along and the reason for it.
Back when I was young and was around guys who were racing "jalopies", "California Uprights" and other "roundy-round" open wheel dirt track stuff as well as some of the early days of drag racing the "dirt/open wheel guys" did require the addition of the steel on top of the cage until one accident where the plate tore loose in a violent "climb over the other guys wheel" wrecks an somehow decapitated the driver (I don't remember the whole story now as it was too long ago but as I remember it was someone I slightly knew) but that is one of the reasons, besides adding weight up high, that I don't think of the top piece but you are right, it should do a lot to stop the cage from burying itself in the sand. Other than the "sand cars" (and I am not sure of that but they are the long travel cars and are probably driven more like a race car) or CWB's rig, I don't remember seeing a rail with the top covered. The open top I have heard as being referred to an emergency escape route (around here I don't remember seeing someone run an "X" in the top of the cage as the speeds are not all that great [55 max but in the few places you can run that fast the areas so busy you don't want to] but "stuff" does happen. Racing is a totally different thing).
I apologize for the miss-use of terms and advice.
You did cover the reasoning for my point though and that was limbs, neck and other things potentially flopping around because of various, not quite as much fun, riding conditions. One of several reasons my cage has the cross-bar up higher. My cage builder also built cages for circle racing (I was going to use another slang term but thought better of it before I wrote it down) and sand rails for the businesses around the sand that rented them for the visitors to either rent to ride the dunes or took people out on the dunes in them.