If you ignore the externalities of winning/losing money the thing that the betting brings to poker that is very hard to replace is the impact it has on the players decision making. People playing poker with "funny money" play the game fundamentally differently to the extent it's almost a different game (arguably worse, certainly less predictable) entirely.

If you take the money out of it you have to replace it with something that matters to the players outside of the game itself for it to work.

(On the lack of information - some versions of poker are different than others but imo Texas Holdem has enough shared information that, combined with the knowledge that people really care about winning or losing informing your ability to read them based on their actions enables very strategic gameplay - the existence of a pro scene with players that consistently do well at a high level of play is evidence of this)

As another aside - I see similar complaints about strategy games that include RNG for things like attack values, and I also disagree with that criticism. I would argue that risk management is an interesting skill that's very hard to include in a game with perfect information.