I'll add what I think is another reason the cinch gets looser: the saddle shifts to where it is supposed to be instead of where we put it. One custom saddle tree maker uses the analogy of two spoons nestled together: Of cutlery and saddle fit...
The curve of the saddle tree has some spot on the back where gravity and the horse's motion will move it. The cinch tends to shift forward or aft to reach the spot of smallest circumference.
To avoid that, I normally put the saddle on with the cinch hanging an inch, then lead my horse through a few figure 8s. That gives the saddle and her shoulders time to get it where it needs to go...a point I now recognize if I use my normal saddle. With most saddles, my cinch or girth needs to angle forward. The sticky neoprene girths I use with my English saddles stay in place well, but my felt (Australian) or mohair (western) ones will slide forward to just behind her elbow. Folks can tell me that is the wrong place for a cinch, but my wool ones end up there regardless.
Also see here: Proper position of a Western saddle Troubleshooting Saddle Fit Problems
If you are cinching up really tight to keep the saddle from shifting, you might consider your saddle fit. I'm guilty
of using a too wide saddle that I really like and padding up, and that my horse works well with...except for when she doesn't: My first emergency dismount, from Mia...while at a full stop!
As much as I like the saddle, it may go up for sale. Then again, I may keep it in case I ever buy a wider horse. Hmmm....
Last summer, my daughter was cantering Trooper up the trail, weaving from side to side to follow the trail. As they got closer, I noticed something wrong. So I held my hand up to stop her, and then pointed out the cinch had come undone & was hanging 6 inches below Trooper's chest. It was banging Trooper's legs with every stride, but Trooper isn't the sort to panic easily...unlike a certain mare of my acquaintance.
My daughter dismounted, retied it, and remounted. But when the saddle fit is really good, and the horse has some withers, you can get by without the cinch. When it works like that, you aren't tempted to offer chicken blood to Norse deities and ask Thor for strength as you go to tighten the girth/cinch.