Building on to this, they should add minor procs to our relic, something that is nice to have but wouldn't be overpowered or break the game.
This way they could still keep their word of having current raid drop ilvl+5 weapons above our relics (so as to keep raid scene active).

Note: Current raid weapons must do more damage than relic because it makes sense.

Our relics however would have a nice proc element to it - has to have a class specific coolness to it (this game desperately need some customization).

I'm using WoW as a reference here, not as a direct apple to apple comparison, but it was these trinket procs that really bring interesting perspective to the combat system (lightning capicitor, anyone?)

For example, think of something along the lines of:

Adding to combat damage or defense:
5% chance of of attacking proccing a chain lightning of 50 potency to nearby enemies. (something like Thunderfury)
5% chance of increasing defense by 5% for 5 secs.
5% chance of regaining MP by 5% (60secs cooldown)
5% chance of block or dodge to proc a shadow that will take 5% of the damage done (limit 2).
5% chance to proc an aura that gives haste of 5% by 5secs.

Visual / aesthetic:
5% chance of attacking to have your weapon switch image with another weapon in your inventory for 10secs (DRK).
5% chance to imbue relic with flashy ice or fire glow when casting appropriate magic (BLM) for 10secs.
5% chance to add more spikes to your dragoon armor. (LOLDRG).
5% chance to turn into Mike Tyson for 10secs (MNK).
5% chance to grow another feather on your armor for 10secs (PLD).
5% chance to have your globe turn into the sun or moon for 10secs (AST).

Again, it doesn't have to be overpowered or game breaking, just something different.
I'm of the opinion that relic weapons should be something cool. Not just a placeholder 'stat stick' until the next patch that it becomes irrelevant as compared to the newly released weapon.

Personally, I really prefer the visual / aesthetic part. It's a relic for crying out loud.

That makes it "on par", sort of with new raid weapons and we don't have to go stress about this topic every single time.
Also makes relic a fun thing to have cause it's cool yo.