To all those saying you don’t “do dressage” to warm up your horses–then my response is you’re not “doing dressage” properly. Good dressage is good training.
Even at the 4* level they are only schooling USDF 3rd level movements. Which basically consists of the horse being on the aids, showing extension and collection at all gaits, and the balance and strength at the canter necessary to both hold counter canter and do some flying changes. I would certainly hope that in warming up to go XC the rider touches on those. No one is doing tempi changes here, even in a dressage warmup (at least not intentionally!). Obviously there would be less of an emphasis on the relaxation and throughness, but the basic principles still ought to apply. These are also all basic flatwork asked at the major equitation/medal classes in the H/J/eq world.
The progression of the dressage tests follow the levels–the levels where XC requires more collection/extension differences also show the same idea in the dressage ring. The levels where maintaining your horse’s canter in a proper balance, whether through counter canter or a change are asked in dressage are also where loss of balance coming to a fence is more influential on XC/SJ.
I’m not saying that’s not hard. I’m riding my OTTB ex-eventer at 3rd level right now and it’s definitely not been easy. But the point of good dressage is to make your horses stronger, more rideable, and attentive to the aids. When dressage is done WRONG it’s certainly detrimental–you don’t want anyone using draw reins warming up for XC but you also don’t ideally want anyone warming up for dressage using draw reins either.
I will also say that I have seen some very scary dressage rounds that, at least in my somewhat limited experience as spectator, tend to map onto fairly scary SJ and XC rounds, mostly due to lack of control and fighting between horse and rider, even with stronger bits. Often these horses are scopey enough to get away with it, but that doesn’t mean it’s pretty…or safe.