Other than a few of the weapons, the current relics aren't too powerful compared to others.
I think they have a lot freedom with new weapons because a lot of the current weapons are valued for other purposes other than just base dmg or dps. (ie: accuracy, emnity, attack power, hp/mp on hit)

Using FFXI as an example.. we had AF armor, AF2 armor, and then eventually +1 variations of both... (Apparently there is also AF3 now? That's wild!)

I think it's a simple idea that they could add an entire other line of RW2 (Relic Weapon), with more a much more challenging quest and much more ridiculous demands.

And directly addressing the OP: From '03-'10 in FFXI, I never saw the mythics or relics ever having a negative effect on other new weapons.. just because relics were far above and beyond most other gear. They were in a class of their own and didn't really interfere much with the rest of the game. I think, at least.