I see a lot split courses in 3 courses: cavern, intro, full (sometimes appr). Here in Europe this is not done mostly.
Cavern is not teached here, we don't have real caverns. If instructors teach cavern, you have to turn around in 20-25m and there is nothing to see, the dive will take less than 5 minutes. If there is a cavern, that is completely unexpectable when you go to a cave, it can be there when starting a dive and gone when ending a dive. So yes, sometimes people get a cavern card, but with only cavern you cannot do anything. So I teach at least to intro to cave. But some go to full cave as this is allowed also. And with only cavern as cert, you have to break your limits already in your course or as first dive after your course.
I did the same when I started cavediving, cavern, intro and full in 7 days (16 dives) and it was really nice to do with a good instructor.
Intro to cave is a course that limits you soo much here that divers will go over their limits in less than 10 dives after the course, agency independent (I have seen this with all agencies, some divers break their limits on their first dive already). In some mines you can only dive with a full cave cert. So another reason to do the full course.
But I want people to have at least adv. nitrox when doing a full cave course. This has to do with the depth of some caves (30m). With air you will get into deco. With nitrox also sometimes. Most dives will not give you any deco, but it is a pity to shorten dives because of.
I never asked a diver to do a course over, but sometimes they told me (happely) they did not learn a lot in their previous course. So we do it then again, but I do not charge or give them a new cert. I always go some extra days to the caves and if not, I have the option to finish in a slatemine.
The first instructor who would say I have to do a course over would be a bad instructor in my eyes. I would choose for another one. But I never had this discussions myself. I only sometimes hear about it.
If you want to do cave in sidemount or ccr, some agencies don't have this option. This is also something to consider.
My own instructor reased his prices from 1500 dollar to over 2500 dollar now over the years. In Europe you pay mostly 1200-1500 euro (so in dollars a little bit more) from nothing to full/technical cave excluding gases, fuel, etc. 600-750 for the intro to cave part (nothing to intro to cave, sometimes you also get a cavern cert) and 750 for the full/technical cave part is normal if you split the course into 2 courses.