No. Taught kindly and properly dressage is not cruel and honestly have you ever tried to force a horse to do anything? Not easy. I tried to remove an escapee from the hay shed once. Didn't want to go, had to be lured back to his stable with a tub of molasses. I was getting nowhere trying to force him. Full weight leaning back on his lead rope and he barely seemed to notice I was there.
I take riding lessons at a school who specialises in competition.
They have several retired horses there who are used to teach beginners and were very successful in their youth. One show jumped and can be found waiting eagerly at the gate the second he sees poles being set up. Gets a right face on if they aren't for him.
He was actually fully retired when he turned 21 only to be brought back into work a year later because he was miserable. Stood at the fence all day watching the others being ridden, it broke your heart to leave him out there. 12 acres of pasture and he stood at the fence watching everyone else work.
He'll probably be ridden until his health dictates that he can't and then decision made as to his future because taking it easy in the pasture was not good for him at all.
He taught me to ride, that horse, and to jump. I learn on a share horse now but miss my lessons with him. He is a kind soul and I absolutely adore him. He is now 23 and mostly only does hacking so about 2 hours work a day but is kept fit and does a showjumping workshop type thing once a month so still does what he loves and can still clear a triple with the best of them!
Another who still works in the school did dressage and can occasionally be found doing piaffes in the field if he sees someone doing it in the school. I'll try and catch him on my phone next time I see him do it. He only retired due to an injury. He's sound but shouldn't be overworked so teaching suits him.
Again he was not happy when out of work recovering. Spent 3 months on box rest and was a liability during that time. Anyone who went close enough got kicked. The minute he was being worked again all that stopped and back to being placid. He's happy. Sometimes still takes students to low level competitions. Intro and Prelim usually but sometimes does more complicated ones with certain students. He thrives on the atmosphere and being the centre of attention, it's the highlight of his day.
And they're far from the only ones. Most have a competitive streak, even in a race across a field when hacking. The oldest boy at 28 yo looks sideways at the flashy little show ponies as if to say 'I'm not losing to you, short stuff. ' and takes off like a rocket. Never seen him move so fast outside of dinner time! He likes to be first, likes to be fastest, likes to be best. Its a high, I guess.
Horses like to have a job. For them it's all a big game. They do these movements to music, the humans cheer and give them attention and treats and fuss over them.
There's a YouTuber Amelia Newcoombe who has a video on how to teach these movements kindly and gently. It should never involve hitting. I believe she does it by touching their feet with a whip and using a vocal cue, a cluck when they lift their foot. The horses I see taught, are taught very similarly. Associate a vocal cue with a movement and reward when they respond.