All this raises the question of why tips get tied to price at all. But it is a cultural norm.

As for myself, I find the US customs with respect to tipping to be over the top (my dry cleaner has a tip jar!), and tends to shift the duty of evaluating the competence of anyone performing a task from that person's management to the customer, which I do not like.

Nevertheless, I am well aware of cultural norms, and equally aware that any failure on my part to conform means that someone who is likely less fortunate than I am will have to make do with less.

So in the case of a "free" drink at an airline club, I have, and will continue to impute some reasonable value of those drinks, and tip accordingly - likely 1 - 2 dollars a drink.