I don't do reining, but I cannot imagine why you would want to have constant pressure anywhere. If the pressure on their sides is meant as a "cue" or an "aid" to signal to them to lift their back, then it would soon become worthless as such because they would tune it out, if it is constant it becomes background noise.
But, if you are talking about using some thigh contact to have a more active and controlling seat, then I suppose that mgith be different. In dressage or English riding, you may have more of your weight distributed down along your thighs, and you may have more grip with your thighs , although in dressage this is not so desirable. I mean, if you are gripping hard with your thighs, your seat will come out of the saddle, more into a half seat like in hunter riding.
So, I have a hard time seeing how haveing nonstop pressure with your thighs is beneficial. Unless the trainer is meaning to have a light grip there, so that you can kind of hold the horse back with your core muscles.