As the title says, many of the relic/mythics would become the best offhand weapons for their class if this was allowed, which I think is a reasonable tradeoff given the amount of effort that goes into these weapons, but also because with the removal of all their function but their damage and attack, the weapons become completely useless in the offhand. The only limitation I would add is to remove the OTDs on relics and the aftermath effects for the mythics when they are offhanded. I believe this is a fair tradeoff.
For relics, the +40 attack and base DMG from an offhanded 99 relic does not usually outdo the 11STR and 22Attack from a STR magian by a large enough margin to justify its removal, and its removal actually makes these weapons worse than said magian weapon, which only take a fraction of the investment.
For Mythics, its more of a case by case basis, but there is actually a not a single weapon for which this would be "broken". Observe:
Daggers:
Currently moot.
-Mandaus are always main-handed with Twashtar plugged into the offhand if both are available
-The same can be said of the Terpsichore
-The Vajra has the potential to be a good offhand, but in truth it would end up simply being a slightly beefed-up crit damage weapon ala Oneiros Knife as it only powers up SA and TA and not overall crit hits. In truth, because of its ugly-high delay, even the SA and TA boost cannot save it in many instances.
Sword:
-If add effect is removed, Excalibur woud barely outdo a Shikargar. Even with it on, RDM and PLDs typically melee with En- spell effects and this greatly diminishes its usefulness.
-Murgleis would serve no meleeing purpose but only allow a RDM to preserve some survivability without losing TP by offhanding it during combat
-Burtgang would be pointless as the weapon is obviously meant to be wielded with a shield
-Tizona would lower the BLU's melee attack damage in favor of higher casting frequency, which is situationally weaker due to the fact that a BLU's swords can outpace their spell damage output
Axe:
-Since Farsha has the lowest base DMG it would be offhanded anyway, thus in regards to an Aymur/Guttler combo, the BST would be sacrificing potential pet bonuses to increase his own damage In fact, if a BST wanted to simply increase his own damage output, Guttler/Astolfo would be superior, and for a pet-centered BST, he would offhand some pet Astolfo with the Aymur.
Katana:
-Kikoku would outpace Fire Arisui on the offhand, but not by much. The paralyze effect is very weak and is often outdone by Jubaku: Ichi.
-Nagi is garbage whether its in the main hand or the offhand.
Club:
-Relic club is always main-handed if its owned when damage is the goal
-Yagrush would simply allow the WHM to continue being a useful support while cast on the front lines. Really, any situation a WHM is meleeing this shouldn't really be a big deal anyway.
Further general points:
-None of the actual good combos will have one-handed jobs dealing damage anywhere near a properly geared relic/mythic/empyrean two-handed job short of things like BLMs meleeing with their Laevateinn and such
-Bards are allowed to gain the full effect of all 3 of their relic, mythic, and empyrean items at once! Is two for us poor one-handers so unreasonable?
-It seems like a nice reward for people that bothered putting effort into all these weapons!
Suggestions, objections?