Banning Omegas from lower rarity tournaments isn't the fix here.
Omegas are balanced when their moves are restricted to the opposing rarity. Your suggestion is problematic in part because the top Omegas tend to fall between legendaries and the new uniques in terms of strength. They can't compete with the stronger uniques or apexes in an advantage scenario; they lack the stat scaling and enhancements to go toe-to-toe with those rarities. Certain niche picks (Masto, Sinraptor) may occasionally be viable, but as a whole they get throttled in those formats.
On top of that, this approach favors a small subset of the higher rarity viable omegas, while completely invalidating the vast majority of the rarity, including those that do better in the lower rarity formats.
The best compromise is to apply the rarity move restrictions to Omegas, not nueter them of their main purpose, which is tournament play.
To be clear, I'm not advocating for completely unlocked Omegas in the lower rarity formats. The powers that be should reverse course on their recent decision, and change it back to how it was. In the event that they don't and keep things as they are (which would be highly undesirable), the answer IMO is restricting a few certain omegas (Masto, sinraptor) from lower rarity formats, not banning the entire rarity outright.
Your suggestion would nuke the entire rarity.