I really don't want to deal with my bank if by some chance amount Y is not what I wanted.
From my (European) point-of-view this seems completely ridiculous, since here I see the actual amount before I have to swipe/insert the card into the device.
However, I completely agree with you that it's not fair to the restaurant/workers if they don't actually get the tip.
Not that I like tipping systems at all, I find them an unnecessary hassle for the customer and detrimental to workers' rights, but if you have to have it I found the system in Canada (at least in Vancouver) much saner: you could key the tip amount into the POS machine when you pay, or directly select a tip percentage and the machine would add the tip for you. Compared to that, having to actually calculate the amount by hand and write it with a pen in the restaurants in New Orleans, blindly trusting that they would eventually charge that amount, looked like... last century.
Checked Monzo again, they have this in american transactions:
> Restaurants in the USA
> Restaurants in the USA are a bit of a special case. The waiter runs your card for the meal's amount and then, after youtip, they cancel the first transaction and charge you again for the meal plus your generous tip.
> REAL TIME
> The problem is that, until the first transaction reverses (10 days later) we don't have a way to tell that the restaurant charged you once or twice.
> Legacy banks will block the initial transaction amount in your account and release it 10 days later, but only the amount + tip will appear in your statement :)