I believe the concern is more that solving who has the best claim to the throne would also prevent some of the in-fighting that has been occurring between the troops, uniting them as a more solid front against the opposition.

( But no, the group should not care very much about who ends up in charge. It's not as if they will be there for the consequences of that choice. )

...she might.

She may be the answer to what ails him though I have heard he has been ill for quite some time.