I never, ever allow my horses to 'let off steam' on the lunge. No way! It might work a couple of times if they're a bit fresh, but then they learn to buck on the lunge, and get fitter so that it takes more lunging to wear then out each time.
My horses can play and buck as much as they like on the paddock, but when they are connected to me via a rope, they are expected to behave.
A horse that jig jogs out of excitement or anxiety will still do it even if you lunge them to exhaustion first. My 11 yr old gets terrible anxiety and there are days when I do feel scared to get on. If I put him in the lunge, he would get even more worked up. So I suck it up, get on and just ride walk leg yields on circles and serpentines until he relaxes and takes a contact. Sometimes it can take 40 mins, sometimes 5, but aiming for relaxation is the key. If I tried to work him hard everytime he started to get anxious, he would probably lose his brain and be a danger to us both.
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I would never longe to exhaustion or to wear them out. And I do expect them to behave, but you can diagnose some problems with moving forward and transitions before you get on. I can completely knock out several problems on the longe line. If the horse bucks every time I push him into a transition on the longe, then he is not ready for me to ride. He needs to learn to push through even if he bucks; something I may not be able to comfortably sit. Then once he accepts that bucking will not get him out of work, and he does the transitions well, it's time to ride.
And for two other horses that I have owned in the past, they are cold-backed and need just a minute to adjust their spine to the saddle, otherwise they will be very grumpy and uncomfortable.
Longing for respect is what I'm getting at, not longing for nowhere.
Although I have quarter horses and paint horses, so maybe that's a thing.