To me, Shu's void isn't actually representative of individual strength at all or wanting to take on others burdens although I will admit that he does try to do this a lot.
I think Shu's void is actually more indicative of his character being highly dependent on others to provide him with some initiative or resolution to act. If we take multiple examples from the series and the way that it was structured in that each new trial practically requires a new void to be used or a combination of pre-existing voids. I'd also like to extend this to Shu's character being on to find some compromise or mediate (to some degree) between others as his void activation relies on some form of acceptance of the other party. The void must generally willingly be given by the owner to be used (tbh, this was my interpretation and I do know that in a few instances there was forced use but thats a different discussion).
Tldr: Shu's void indicates he can be described as cooperative and submissive at least in line with my previous point. As the series goes on he loses this submissiveness and becomes willful if not arrogant but eventually humbled by the events. I think the final episodes really stress he needs others and he settles down to an almost meek attitude about his relationships with others.
On a deeper level I'd say that as Shu is the main character and given the way his void works with others is that the message of co-dependency of all members of society for the achievement of a specific goal. Furthermore given that his Void is the 'Power of the King' there can be two further interpretations:
- the power of the king is a absolute power that can manipulate, order, influence and control others.
- the power of the king by itself is useless as it is dependent on the acceptance of it by its subjects, and through that acceptance, conformity with the kings demands.
Sadly I can't say much for Inori except that I do think she is quite bold in that her ambitions and willingness to be party to certain things for the sake of a goal is a standout feature of hers. She's willing to take on a fair bit of burden.
Take my answer for what you will, it's also quite likely i'm completely wrong :P