That could be the nuance thats covered in the books, which I have not read, but is not shown in the TV series. My surface interpretation of the relative power as it's presented is this:
-Taiko has the ultimate authority, but because he's underage, he and his mom sit idle with their executive powers.
-The 5 regents are next in hierarchy. In theory equals as they abide by contracts and consensus, but obviously have soft power ie influence.
-Their army/fiefdom backs their power only if push comes to shove. Meanwhile, in the political sphere, there is ample room to jostle for lead. Ishido sat at the literal head of the room during the meetings.
Mariko did try to press her noble lineage ("Im the daughter or Akechai!")... but that family was dishonored, she was almost run out of the empire, and shes married to a samurai, not a Lord. The presentation of her importance just didnt seem consistent throughout the show.