More in the realm of retaining sanity after the contract, or convincing the spirit to cooperate with something that will change the kingdom's perception more quickly.
Ah, understood.
I believe I remember that the 'loss of sanity' aspect was from the sheer amount of time passing upon becoming immortal, to the point that the Contract-wielder loses all connection to other people, and by association their own humanity. Watching enough generations die, and people take on the same sort of importance in one's scope of things as insects do, for us.
That's not something that can really be helped, in that case.
As far as the spirit intervening with the governmental system of the kingdom in a direct fashion - that would be a step further than even having Euphie be "adopted" by the Crown and then taking the throne for herself as an immortal Contract-wielder who can use the Spirit connection and her own magical potency to silence any dissent from nobility. Euphie is already in-effect strongarming the system and forcing her way through, just on a level of "legitimacy" that ties the nobility's hands, especially as there's precedent with the Spirit herself being the ...I believe 2nd ruler of the kingdom upon its founding.
Whether the Spirit would be ruling herself or not, I think any further interference would be too much for the nobility, and could risk a breaking point if Euphie and Anis try to force large-scale changes through the "credibility" of the Spirit. The nobility are still very much self-interested, and would only bend the knee so much to an outside power mucking up their current influence of things before they'd retaliate - with the worst case being open civil war, which ...is bad.
But if it hasn't been touched on already, maybe it'll come up in later chapters, as to why the Spirit can't do something. It might be as simple as "it's not in my interest" from the Spirit's perspective to go interfering in mortal statecraft, and the Contract is simply the most she's willing to do.
But, who knows. The other side of it is that, either way, having something come up
now would kind of invalidate the whole fight bewteen Anis and Euphie that just took place. And both are intelligent enough that I'd wager one of them would have thought of some way of resolving the succession issue using the Spirit, regardless of the Isekai Angle.