Here's the thing about Honor's truest surge. Remember that the Stormfather said that Dalinar's powers wouldn't work. So I more view it as the fact that it's Honor's truest surge AND the fact that Kaladin's spren is an HONORSPREN. Which is of Honor. Retroactively, you can look at the same thing for Lift. Her surge of Progression works because it's Cultivation's truest surge AND because her spren is a CULTIVATIONSPREN, which is of Cultivation. And that both of them are invested enough to stay awake in the tower.
This can really cause a reassessment of the surgebinding magic system. Instead of 10 or 9 plus 1, it's 8 plus 2 (2 meaning Honor and Cultivation), which is more in line with the basic allomancy system. Then imagine if voidbinding is really 8 plus 1 (1 meaning odium) and it will turn out that the Rosharan magic system in closely aligned to the rest of the cosmere. This most likely won't be actualized in the canon and currently has some holes in the theory, but it seems like something Brandon might pull and it seems like it may have some truth in it.