I do see an incredibly obvious reason: my agency that I have as a player playing in a given tabletop roleplaying may not be strictly limited to what my character does. That's why. It may not make a difference to you, but that distinction does matter to me. You said it yourself:
I think this point should ideally sit outside the question of comparative agency; we're dealing with two separate design goals (regardless of how effectively implemented) that produce different game states. Agency can still be compared between them, but not as a function of the actions available. Instead, we should be talking about the relative impact of those actions on the proposed goal of both games. That goal is the sticking point: I suspect it's sufficiently different (my earlier point about ludic vs. narrative agency was, in retrospect, driving at this point) that directly comparing what's achieved by a given action isn't meaningful.
That is, if you transposed an action from a game that allowed for player/character separation in action declarations to a game that previously didn't, obviously that new action would be a significant increase in agency, but that isn't actually the meaningful point of comparison. Instead, you should be looking at the relative impact of those actions in their initial context.
Player agency is about what we do as players in the game. What I can do as a player playing in games like Fate, Cortex Prime, Stonetop, Torchbearer, or maybe even Daggerheart is not necessarily limited to what I can do as a player playing at your D&D 5e table. The bounds of my agency as a player playing these games exist outside of the scope of the agency I may have playing in your high agency D&D games or Bloodtide's. I think that any definition of player agency for tabletop roleplaying games must be inclusive, rather than exclusive, of all these different modes of player agency. The problem with your definition of player agency that conflates player agency with character agency is that defining player agency strictly in terms of character agency excludes these other modes of player agency that I may have as a player playing these other games. For that reason, I don't think that your definition is a good or functional one.
To be fair, it's clear that the player agency of a player in nearly any game exceeds that of Bloodtide's.
At the risk of invoking its own acrimonious tangent, I think my point about context is well demonstrated by skill challenges. I have railed against them as a design in the past on the specific grounds that they decrease player agency. They abstract the distance between the current board state and a goal and limit the effectiveness of player actions to resolve the situation through setting thresholds independent of the actions taken. Depending on the precise iteration, they sometimes include enforced metagame requirements for group participation, and/or may end up altering the difficulty of a proposed course of action through reference to the level of challenge, even if the action could be correlated to a known, fixed difficulty. Generally, I find they limit the ability of players to best defeat obstacles, relative to an alternative system that specifies the result/effectiveness of actions preemptively thus that players can string together whatever series of actions they believe will best overcome a problem; the most obvious way this is true is that variance in the amount of checks between a player and success as a result of the player's actions is intrinsic to such a system, and impossible ina skill challenge system.
However, the precisely opposite argument is routinely made about them! Because they allow for resolution of a task with a wide, array of declarations that could encompass more actions than are encoded in even an elaborate skill system, they provide more player input into what happens. Thus, agency requires an understanding of the goal player actions are evaluated in context of.