I had a horse as a kid who I did the big jumps with and he used to get visibly “off” on the side that had no elastic on the girth. Quit using a single/one-end elastic girth and never had an issue with him getting sore and tight on that one side again. Never used “uneven” girths since.
EquiSport - look at the Le Tixerant girths. They’re designed with that principal in mind (the elastic/stretch part is in the center of the chest). I have one that I dislike because I feel like my saddle moves more with that girth than with a regular anatomical girth. But it may be what you’re looking for?
To those who use cord girths, I want to say that your’e basically using the equivalent of a full elastic girth. Cord girths have a ton more natural stretch and give than a solid leather girth. I think that’s a bit of comparing apples to oranges. A cord girth, despite not having elastic inserts, is definitely not the same thing as a solid leather or nylon girth without elastic.
I prefer double elastic girths, and all of my horses go in anatomical girths (only jumpers, though, as I primarily jump - though I also have a County Logic for my one dressage saddle). I am guilty of wanting to crank the girth down on my horses who are a bit of a tougher fit saddle-wise, but had an interesting lesson recently.
My super narrow, high withered youngster developed a huge hematoma in his girth area when he was off with a [less-than-stellar] trainer this summer. He got a bunch of time off, but still had a huge “boob” when it came time to go back under saddle. So I rode him in a saddle with no girth for a couple of months (video of him trotting around girthless here). I’ll be darned if I couldn’t even tell the difference between having a girth and not having one (other than the fear of being launched a mile high should he suddenly have a bucking fit or do something unpredictable - which would not be totally out of character for this guy). Now it’s largely because he’s so narrow and high-withered, but I could even mount relatively normally without the girth. When we started jumping again I had moved on to a cord girth, but I still have it super loose. Totally not an issue.
It’s made my rethink my need for a “tight” girth, and I’ve eased everyone’s girth settings a hole or two lower since.