Not sure what you're aiming at: shooting left-handed with a left-handed bow, or shooting right-handed with a left-handed bow. In my opinion, learning to shoot left-handed with a left-handed bow is a wonderful idea for person who normally shoots a right-handed bow. It helps keep your body in better balance, and adds a useful skill that might come in handy someday. Plus, it's nowhere near as difficult as it might seem to be before you try it.
Shooting a left-handed bow right-handed is problematic for most people. Bows are designed the way they are for a purpose, which should not be ignored. Grips, other than straight handled longbows, are contoured for one hand or the other. If the shelf is on the same side of the bow as the dominant eye, the non-dominant eye would be blocked, interfering with binocular vision. It seems that those who use a thumb ring release prefer to have the shelf on the same side of the bow as their dominant eye, but I’m not sure why. Joel Turner used to shoot that way with a thumb ring, and may still do that. Possibly he has a YouTube video that would explain his reasoning.
The bottom line is that traditional archery is noted for being a pragmatic sport, with rules being more suggestions than mandates. If something works better for you than it does for 99% of other people, more power to you.