The only job with a 90s cycle that matters is Monk, because Brotherhood is 90s. Aligning our burst with, say, Warrior would be meaningless - the Bard dealing more damage and the Warrior dealing more damage at the same time has no inherent value, we aren't buffing each other and Battle Voice doesn't even work on them. The other three tanks are 60s cycle jobs, as much as Delirium might make it look otherwise.
*If* there were more than just Monk, if like four or five jobs had raid buffs that went out at 90s intervals, I'd totally understand the push to align Bard with that. But it's a mirage, this idea that "some jobs are 1m/2m and some others are 90s" just isn't real. Only MNK and WAR are 90s and the latter doesn't interact with us. SE could decide to add more real 90s cycles, or they could move MNK and WAR off of it, but leaving those two hanging in particular is weird.
BRD, for what it's worth, hardly qualifies as having a "burst" right now compared to those other two, we're pretty much just a sustained damage job that presses Barrage sometimes. So even if we were transformed into 90s, with the kit as-is, none of the other jobs would care. Bard rotation vs. (crit) raid buff alignment was extremely valuable in Stormblood, but in ShB it's barely relevant.
As for the passive song buffs, I agree it'd be nice to find a way to make them work, but with the 100% uptime of songs, so the buff has to be miniscule/limited to be safe power-wise. If they had durations to tweak up the power and started on song use, the relative lack of control over timing songs means you'd have problems getting them into useful spots.
That's what my
somewhat-wild BV rework idea is about - it uses BV to carry on the spirit of the passive song buff in a way that can circumvent these barriers. Would SE do it? Dunno. But I think most players would like it more than the current setup.