So it seems there is no use to upgrade the power of the skald songs?
 

As the topic says. Right?

Not that I noticed. That 10% bonus is multiplicative, not additive, so after spending your hard-earned runes for the next rank you won't see more than a 1% boost to most skills. For example, the initiative song goes from a 19 to 20% chance to happen and the 7% chance to stun song doesn't move up at all.

I might be missing something though... because once I realized that I loaded that save really fast. :)

Same, in my experience. I upgraded to Level 3, noticed no significant difference and reloaded. I have better things to spend Spirit Runes on. For now, at least.