I can not make any comment regarding the services offered by the recovery companies. I guess what you are offered is related to the premium you have paid.
However, I assume everyone on this Forum has actually made an attempt at changing either the caravan or even their car wheels???? Much discussion has already been made regarding jacking of caravans, and how difficult it can be, but has everyone seen how heavy and cumbersome car wheels have become, especially with the low profile tyres. In addition, can the wheel nuts even be undone using the puny device supplied. I have an extendable wrench for my motormover which I also use for the wheel nuts and even then it can take a hernia inducing heave to get them free. These are retightened to the correct torque but tighten themselves with use, especially if the wheel is alloy. Use of copper grease will help but you cannot overdo that or you may get the wrong torque figures.
No disrespect to the ladies, but unless they are 'Pansy Potter, the strongman's daughter' (Beano), they should just call the recovery service, I don't think they would abandon you whether or not a spare is carried. Of course with a caravan puncture you can always leave it on the jack at the side of the road and take the offending wheel to be repaired. You just hope the van is still there when you get back, or leave a minder.