Humans would end up with huge piles sometimes (they often ought to be spending them anyway).
The reminder could certainly pop up -could maybe even go there when you hit end turn like it does for idle heroes.

I guess that a holy order could get to the point that the player doesn't want to change it any further. Then the notices would be annoying. But that seems like a smaller problem than missing the chance to spend points.

I make it a habit to click on empty ground so I can see the alert messages. Holy orders which can be influenced are listed there.

I'm slowly learning to watch the little red boxes at the top of the screen, and to ignore the popups as unreliable. I'm even learning the abbreviations. CNIO is the crucial notice to spend influence.

Still, it's a nasty "gotcha" for new players.

I was unclear. If you click on threats on the side of the screen, it will always show when holy orders can be influenced.

https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=3147266443

The pop ups are not reliable because they don't appear if you gain enough influence from an agent's challenge. That's probably something that should be addressed, I agree. The pop up message telling us we can influence a holy order only appears if the passive elder influence gain per turn causes it to hit the cap.

Ah, I see. I should check those messages every turn. I'm just finishing up my third full game, so there's still so much to learn.