The problem is the way WoW is designed and what 'Support' actually means versus what people expect it to be.
Bards as a class have an association with being Support classes. You are correct that this doesn't have to be how it is translated into gameplay mechanics, but it's difficult to actually make an argument out of this without actual mechanics to discuss. We can just blanketly say that this class could have one of the best support toolkits in the game, but what does that mean overall? WoW has persistently *removed* the support aspect of the game and homogenized the class and spec system to a bare minimum of support, varying each expansion. It shows that Blizzard doesn't want to design WoW around co-dependancies in raids. They *don't want* niche Support classes the way they existed in previous iterations of the game, like wanting Druids for Innervate or bringing Shamans for Blood Lust. They even effectively toned down the requirement of classes bringing unique buffs to the raid.
They're also laser-focused on making roles very pure. Shadow Priest used to be considered a heavy support DPS role, but it's now designed to be pure DPS with very minor emphasis on the utility they bring. That's the way all classes are being addressed across the board; so if we are to consider any Bard concept it would have to be on the basis of it bringing a unique theme alone, and not on the basis of it providing a new standard or providing great utility. The way the game and roles are balanced, they'll simply have to be competitive DPS and Healers on their own merit. I don't think there's any way to properly associate them being 'best support toolkits' any more than you could associate that to Druids having innervates and battle res or Warlocks having soulstones and summons. They'd just be associated as unique Bard class mechanics.
The issues I see is that without a true Support niche to carve out its own, I don't think many people will be very open to a Bard DPS or Bard Healer class as a main-pick. It's not even as strong a concept as say Monks in WoW, and we all know how popular Monks are in WoW. I see the Bard concept missing the key 'Rule of Cool' gimmick that would get people hyped up on choosing them as a main, mostly due to its obvious associations as a Support-type class and not as a mainline archetypical DPS or Healer. It's a hard pill to swallow if Blizzard chooses to pour resources into designing a proper Bard class knowing all the other potential class concepts being passed up just to add (what I personally consider) a B-tier concept. Of all the potential classes to add to the game, why pick a Bard that has no proper Support role to fill? That's what many people will be expecting and asking. It's not a matter of whether Bards would fit into WoW, but a matter of whether they should be on the shortlist of classes people are anticipating to play. And as I explained, in terms of gameplay all we would be getting out of a Bard is its musical themes since the game is already fully embracing the Holy Trinity style of play.