. . .there are ROV's that use a fine fiber-optic filament which plays out off a reel (just like a primary reel) behind the ROV, and therefore line handling is not a huge issue. But, I have never seen a ROV that would fit through a 4" gap.
Sure, the ROV could be sending a digital signal back through that fine fiber-optic filament, but that is not all there is to it.
Fiber cables in an interior location, under zero stress (as in they are tied to and run along cable trays, and do not have to even support their own weight), are incased in several layers of fiber-mesh coaxial casings, and several layers of special rubber coatings that do not allow the cable to bend anywhere close to a kinking radius. In general, the spec is an 18" radius bend. These non-stressed cables are 1/2" in diameter, and protect fiber optic strands half the width of a human hair.
Fiber optic cables that are expected to be strung have wire mesh coaxial and usually several of them, depending on the expected stress and movement of the cable. For 'tactical' military situations, fiber-optic cables that go simply from one van to another about six feet away are 3/4" to 7/8", since they will withstand wind and rain and freezing.
So, not knowing anything about this underwater ROV, that has to drag a tether, and that tether is capable of being drug almost 2k feet, that the minimum cable diamether is 1". I'll also bet there is a co-strung stainless steel cable (for strength) of up to 1/4" diameter.
Now, if this thing is powered by electricity, you will also have a 3-wire or 4-wire (4th wire circuit for controls, but it could be one of the fibre strands) also running the tether length. If the ROV is battery controlled, yikes on the size of the batteries!
Now, as I remember the military tactical fiber cable, it weighed about 15 or so pounds for that six foot cable. Let's remove 3 lbs for the cable ends, and 12 lbs / 6 feet is
2 lbs / foot! . . . Whoa. And how many divers will it take to feed this cable anaconda through the almost 2k feet of cave?
And how fast do you move this behemoth? Twenty, twenty-five feet a minute? 1900/25 = 76minutes of hard work. How much gas is that going to take?
Do the math, and it comes out that you cave divers are a crazy bunch -- thank God for those of you that tackle this stuff. My prayers are with you all.