Allowing other jobs to use instruments just for a small, small, tiny part of the game (i.e Grellow) doesn't make sense to me. Instruments are what make Bard unique; take them from the job, and you're left with nothing. Bard doesn't have spells that aren't songs. A white mage won't cry about another job having cure because there are ~16 jobs in the game, and cure is something that shouldn't be specific to one single class; however, WHM excels at said spell (due to high MND, MP, abilities, white-magic focus, etc). Bard won't cry if another job can sing one song as /brd, but BRD excels at songs (due to instruments).

If we really want to start talking about a bard losing uniqueness because of Grellow, let's also talk about how another class can get a wyvern.