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What I have in mind is that you do not touch the stages except if you bailout, so you need OC gas only for the exit + problem management (like hypercapnia, but of course there is more depending on the cave: flow, eventual silt out in highly silty caves, restrictions, etc.) when diving in CCR.
For example, imagine a dive with 2 stages in CCR. You can leave the first stage at a distance that you can cover breathing it (it is full when you leave it, since you are breathing from the CCR). Then you can continue the dive based on the amount of gas in your second stage bailout (or backgas if your configuration is GUE style); then you need to come back. Of course, you want to add some safety to deal with problems. And, of course, oxygen and diluent adequate for the dive, but I consider them part of the CCR.
So you cover with 2 stages (or one stage + backgas) + CCR the distance you can cover in OC with the two stages (or one stage + backgas) minus the gas you want to save to solve eventual problems.
Assume open circuit, same dive. You would need for the same dive 4 tanks minus the amount of gas you want to keep for reserve (which is at least one third of backgas).
So basically you are right in this range, because you would bring, assuming doubles, two stages plus the backmounted doubles - which is almost equivalent to a CCR set except if you go for something ultracompact, right?
But if you add another stage in CCR, you need to add two stages in OC. However, assuming shallow caves, and depending on your SAC, we are in the range you mentioned (5000ft+) - and I am rather sure if you add calculation for reserve gas we end up to your result.
Again, I am overly-simplifying the management of problems (we all know, thirds or stricter rules in OC, account for hypercapnia or other problems in CCR, eventual morphology of the cave, flow, etc.), I would never plan a cave dive without taking into account more factors and writing down all I need, but I see an advantage in long penetrations, which is what I meant...
With Cave CCR there is a minimum of 2x bottles to carry, no exception. If you say a "standard" set of doubles are LP104's that hold ~260cf of gas when cave filled that would give you ~174cf of exit/reserve gas and with a CCR with 2x AL80's that gives you ~150cf, so call that close enough. So for anything within the radius of LP104's, you're carrying a LOT more gear because a backmount CCR is effectively equal to a set of doubles and then you need the pair of bailout bottles. On a Sidewinder then you can argue that it's LP85's plus the breather so it's a pretty negligible increase in equipment, or if you have a rack mounted unit then it's pretty comparable.
If we look at LP104's + 2x stages we have a total of ~410cf of gas and would be ~280cf for straight bailout, not including any factors for hypercapnia. 280cf would typically be LP85/HP120 + 1x stage or 4x al80's. Sure we are carrying a bit less CF of gas to your original point, but it's about the same amount of gear, and once we add in the factor for hypercapnia resolution we are at the 2x steels + 2x stages, or 4-5x AL80's and now we are back at nearly the same amount of gas that we started with on OC. The CCR's start making sense from an efficiency point after LP104's + 2x stages, which if we were talking about this in 2015 would have been a BIG dive at around 4000ft penetration in Florida caves. With CCR's and DPV's becoming much more common it is not perceived the same as it was, but that's a long way from the door. Obviously scale that distance up or down based on the depth of the cave, personal kicking speed, or factoring in a backup DPV, but no matter how you skin it, that is not a "normal" cave dive for the vast majority of divers.
If we sidestep over to the ocean, you're still carrying all of the same deco bottles, though you will typically be ditching bottom stages, but it's not really saving a lot of gear in the water.