It is true that WAR currently can proc most !! for red, but it is absolutely not true for blue. This Job Ability would effectively remove BLM, COR, DNC, DRG, DRK, MNK, NIN, RNG, SAM, SCH, SMN, THF, and WHM from ever being used in Abyssea again for procing blue. That alone unbalances Abyssea's need for anything but WAR and a healer.
They did have this in mind when they designed red !! to be general WS that can be used by most jobs. It's red specifically because this is the key item proc that can be used by everyone. Whereas blue !! are from job specific WSes for things that are gear drop specific. The harder things and more sought after things. In other words need a higher variety of jobs to have an increased chance of drop rate.
What you don't understand is what you just said was the reality of things even before Abyssea. Everything was limited to a very few selected jobs, restricting players that don't have those jobs to never be included. Yes Abyssea upset the balance, or lack of balance that FFXI originally had. At least now with the !! system, the people that only have jobs like PUP can be invited to participate. This greatly rebalanced the game so that the not so popular jobs are now viable in certain roles.
While this is true for you and a lot of people, this is not true for everyone. Not everyone has the luxury or the ability to be in lowman groups. Just because this change doesn't do anything game breaking for you aside from it just being "cool", doesn't mean this doesn't effect other players on a massive scale. Not everyone can lowman things simply because their jobs of preference are not the preferred jobs of the general populous. In a single swipe, you completely denied thirteen jobs from participating. That translates into a lot of players missing out on content just because you just want to be cooler.
Just because WAR has access to thirteen weapon groups does not mean that they have become or should become a master of all of them.
What makes a job unique is more than their Job Abilities. Their ability to use job specific WS greatly effect what defines them as that class. What you've essentially stated is that every job should have access to every weapon, because it's not the weapon that defines the job what-so-ever. Yes, what will DRK be when WAR gets access to Guillotine? A WAR that rarely uses it's Job Abilities, with just slightly higher skill as well as access to some magic, but lacks every single thing that WAR powerful. Yes that's defines a DRK, his ability to Soul Eater; because we all know that WARs are equally good at using scythes as well.
Just because WAR has access to so many weapon types and SCH has access to so many magic types, doesn't mean they're meant to be used in all situations, or even in any situation. Just because my car has four wheels doesn't automatically make it just as effective in the water as four wheeled cars specifically designed to be amphibious.
WARs are very versatile, but they aren't always asked to come to certain events due to other jobs simply because of their differences. SCH's the same way. SCH can both nuke and cure, but it by no means can replace either a nuker or a healer. Your suggestion is simply saying SCH by DESIGN should replace BLM and a WHM. WARs should replace all other DDs, tanks, healers and nukers. I mean, they're DESIGNed to be versatile. You're the one that said,

