If you are going to rope something, you cinch up tight. Like, REALLY tight.
You don’t get on, gallop off, and rope something, though. It is never appropriate or polite to just pull that cinch up as tight as you can get it, without the horse moving around, taking up a bit, moving around, taking up a bit more. So I wouldn’t tack up western like I would english…saddle up, lead the horse to the arena, take up the girth and get on…warm up a bit and possibly tighten the girth mounted. I’d tack up, and take up on the cinch four or five times before I got on, having the horse move around and get comfortable before I took up again.
My ‘withered’ horses, don’t need a western saddle quite so tight, even if I will mount from the ground or go up/down through steep country. My two beer-keg/propane tank, not-much-for-withers mares, you’re going to have to cinch up a little tighter for safety. And they also need to toughen their skin a bit, if they’re going to be ridden regularly, or they’ll get cinch sores.
I’ve got off the TB gelding, with a cinch that could ‘come up two or three holes’ if it were an english/elastic end girth, but the saddle fits very well and doesn’t move.
If you have (leather) latigo on both sides, the leather will stretch a bit to accommodate the horse’s breathing. A merino or alpaca cinch will also have some give, so even roping-tight, the horse can still breathe. The merino/alpaca fibers will also give a slight bit of grip to the cinch where it will interact with the horse’s haircoat, which will help a bit to keep the saddle in place.
I don’t like nylon web ‘latigos’ or thick ‘half breed’ offside latigos. They don’t stretch. I think the inexpensive rayon cinches will stretch a bit, but the nylon-core neoprene ones, or the felt-lined nylon ones won’t. So I wouldn’t use the nylon, or if I did I wouldn’t cinch up tight enough to rope with them. Neoprene, I might use if the horse were already galled a bit, or on a particular horse that was allergic/sensitive to wool or some such, but I haven’t come across the situation myself.