Ok, to anyone who believes paying minimum amount is not optimal, I offer a challenge:
Assume that $1 is the minimum amount you can pay for bottle imp.
Construct ANY scenario where your opponent has bottle imp, you have played cursed bottle, and would be happier if your opponent had paid $1 for bottle imp than if they had paid >$1.
Hard mode: Same as the above, but you are playing open-hand dominion, where you can always see your opponent's hand.
I believe normal mode to already be very difficult and to have no solutions which are not extreme edge cases. Prove me wrong.
Actually, I believe both modes to be impossible without assuming that you are a bad player
That's super easy. If I misevaluated the strength of Bottle Imp, not having the option to get it is actually good. Not at the very moment I have to make the choice, then I am pissed. But if I win the game due to this lack of an option I see that it was in hindsight good.
It is like playing with people who have never played with Thief or Pirate Ship. Suppose you play a variant in which they get the option to use Pirate Ship and Thief as two extra, private piles. Of course they are happy, more choice is never a bad thing according to you, right? But because they are unfamiliar with the cards they overvalue Treasure-trashing and lose the game.
Now I guess you would label them bad players but they aren't, they are just unfamiliar with a particular category of cards.
Bottle Imp is also a new card and like with all new cards even good players will frequently misevaluate their strength until they have enough experience.
I totally agree with you that if the game consists of good players who have played often enough (and given how complex it is and how harsh the -13VPs are, 2 or 3 games will definitely not suffice!) with Bottle Imp and rarely misevaluate it, paying more than the minimum amount is probably wrong.
But if you are unsure about it and would like it most to only get a few plays out of Bottle Imp and then hope to get rid of it, creating the option for your opponent to make you achieve that very goal isn't bad play but good play. Other factors like psychology and his deck state also influence this decision. If he is in dire need of gaining and if you can "read" (we are human beings and prone to biases, I know e.g. whose players in my gaming group are village piel drivers and this knowledge informs my play) him and know that he will go for Bottle Imp, paying $1 or $2 extra for Bottle Imp could be a smart gamble.
So yeah, it looks like this entire argument boils down to differences of perspective: theoretical or pragmatic. As God isn't in my playing group I have little interest in hypertheoretical arguments that assume perfect play.
Do you play chess or are you married? These are the most obvious examples that illustrate why lack of options isn't automatically bad. While a chess engine only cares about finding the best move according to its evaluation function a real human player sometimes plays a slightly inferior move that creates options for his opponent to go wrong or a very inferior move that creates the option for this opponent to go very wrong aka a trap. So even a deterministic game like chess features risk management.