Bard procs have little impact on damage variability

[Absurdity]

Obviously it's intentional. SE has long tried to keep jobs balanced (by their metrics, not players').

In fact, I would argue this is why they changed BRD procs to be a fixed proc rate as opposed to being influenced by crit, which they were in the past. That meant you could literally increase the proc rate by stacking crit. To a certain extent, you can still increase the procs on many jobs indirectly by stacking Skill/Spell Speed, because the faster GCD means more rolls at trying to trigger a proc over, say, a 10 minute duration, but in many cases this is deemed not as good as just stacking Crit, DH or Determination.

Repertoire procs are seemingly on their own tick system, which is just server ticks but counted from the moment you cast a song, so every 3 seconds. That would mean Sks does exactly nothing for that part of the job.

You could technically get more Refulgent Arrow procs from the increased amount of Burst Shot casts and slightly higher DoT damage, but that's pretty much the only thing it does and clearly not worth it.
The only reason bard wants any skill speed is for better cooldown alignment.