Does structure damage account into champion balance?
Mostly.
In some cases (release Rengar) it wasn't thought out very well.
But it's generally a prominent consideration with designing several champions, as if you give a big AD/AS steroid to someone like Tryndamere or Rengar while giving them garbage team-fight potential, all they're going to do is back door and split push. The optimal play-pattern for such champions quickly devolves to a point where getting killed attempting to split-push is less of a risk than even trying to team-fight.
This heavily explains why Yasou's AA steroid is crit and bonus armor pen - 2 steroids that do 0.00% more DPS to towers. Riot could have easily givin him the same DPS with AD or AS steroids (like they did with pre-rework Yi and pre-rework Fiora and pre-rework Sion and a lot of champions that generally needed reworking).
Also: it's worth noting a lot of the champions you mentioned specifically don't itemize for tons of AD, leaving their item-boosted vs. tower damage pretty lacking.
In the case of a pure AD champion like Yasou or Vayne: super-steroided damage vs. towers would be overkill (so crit instead of AD/AS) as would Tumble damage, because pure AD itemization gaurantees a solid tower-thrashing to beging with.
However - with someone like Nasus, Garen, and Xin (at least in competitive where he's forced to build more tanky than DPS), it's nice for them to be able to lay down some hurt on a tower rather than resorting to a death of a 1,000 cuts to bring it down (or just needing the team's marksman to hold their hand).
Game is won from blowing up a Nexus after blowing up towers after all.