I would argue a princess competing for the throne in a world with a royal family that isn't a puppet would have all of that available. Not to mention he was worried because the Chancellor can do nothing and is less influential
Joining the princess would make him hiding the fact he's an UR grade pointless. She wants him as a bludgeon against the other heirs.
The fact that she needs him as a trump card suggests she doesn't have all that much influence in the first place, otherwise she'd already be the Crown Princess and not have to resort to recruiting/marrying a UR grade summon.
Where the hell did you get that the MC's worried over the Chancellor doing nothing or is less influential? A previous chapter outright said the Chancellor is holding the country together.
Since the Chancellor had already warned one of the royal Princes to not touch the MC's waifu, and how the Chancellor is basically running the nation shows the Chancellor has far more influence than the 2nd Princess does.