While it means that you'd be pressing 1 fewer button in solo combat, nothing else about this is necessarily backwards nor stupid. You can either lose proportionate potency from the rest of your toolkit, or benefit from your own songs. Balance will be the goal either way. You just need to decide whether you want 100% song uptime (even prior to WM being available) to further be a requirement for your full DPS (e.g. balanced around it, and penalizing any form of song saving, along with Bard during leveling, prior to having all 3 songs).
Take Brotherhood for example. If Monk was balanced around receiving the damage buff itself, it would simply be harder to time it appropriately as not to waste stacks, given that you'd have the same very rigid windows placed around it, then, as any other damage-modifying CD. Sure, now you use it in solo content, too, but it's only more annoying in group content, and your DPS, ideally, goes unchanged (having simply taken from somewhere else).
Read again. I said that if you had the crit and direct hit buffs, you would be balanced around... having the crit and direct hit buffs, i.e. your DPS would be further dependent on Battle Voice. It's irrelevant to your actual throughput. The only change would be that your DPS has additional dependencies. At present, BV can always be popped whenever it would best aid the party; you are irrelevant to that, and thus a bit more freedom in how to deploy it. At present, you are not effectively losing 3% crit whenever you do not have a song active (e.g. saving it briefly during a dungeon run for when you can actually reel in the multi-DoT rewards, or when you're still leveling and don't have all three). Gaining effects for an ability and losing effects from the absence of an ability are just two sides of the same coin. One is simply dependent on the skill, for better or worse, increasing depth and reducing leniency. Whether that improves gameplay will depend on the ability, its surrounding toolkit, and likely on player preference.
It is not, however, an issue of throughput until such time as development decides that Bard is undertuned *and* that more general ways of buffing the class would be too powerful or otherwise undesirable.