First off, my appologies to the OP that this post pertains entirely to a somewhat off-topic side conversation. I have no useful insight into the original issue.
Searching your inventory wouldn't even help, at least not very often, as most commonly the missing item has been sold or converted.
I know if a piece is dyed a different color it will just give a warning, but still equip, but I'm pretty sure any piece being missing will cause it not to equip anything from the set. I've had a gear set fail once because I was missing the necklace. I'd replaced a NQ necklace with a HQ equivalent, updated the gear set I was using at the time, and sold the old NQ one before realizing it was also used in another gear set I hadn't updated.
Well, as someone who's done this more than once, I find your characterization of it as "stupid" a bit presumptuous. Primary weapons are replaced every two or three levels, and it's the one item that we clearly know will never be useful for another class later, so is completely obsolete as soon as it's replaced. It's easy enough to replace your weapon, sell or convert the old one, and forget to update your gear sets to match. (The last time this happened to me, I'd replaced my THM wand and converted the old one. I did, in fact, remember to update my main THM gear set, but had forgotten that my cosmetic gear set with the striped swimsuit had also included the THM wand.)
That said, I do like your solution to the problem. I wish they'd just let us replace the missing item from the gear set rather than having to re-create the gear set from scratch.
A number of the set wouldn't work, as some items will be part of multiple sets. (Consider an accessory that boosts craftsmanship, for instance. If your crafting classes are near enough the same level to all use it, it's likely to be part of eight different gear sets, one for each crafting class.) I would, however, very much like to see them add some mark on the gear's icon indicating that it's part of a set. Even if we need to sort out for ourselves which set or sets it belongs to, at least we'd know to do so before selling or converting it.