Not in the Netherlands, no. The card can be a bank card, and you can be billed at the end of the month automatically through direct debit.
It also wouldn't work as you describe, as the terminal at the point of entry doesn't know how much to charge you since it doesn't know where your journey ends.
Some transit systems work by putting a hold on your card for a nominal amount. When you finish your journey it then only claims the cost of your journey
Holds don't really show up in the monthly statement. At least not in the cards I've had. It's a functionality for merchants to say "I'd like to charge this customer up to $500, would she be good for it?". If the CC company says yes, then the merchant knows they can do so. E.g. car rental companies do this for potential damages. Up to a week the merchant can charge the actual amount (usually less) or just release the hold.
Holds are a credit card feature, GVB is a Dutch transit authority, so they're more likely to be talking about bank cards, ie. debit cards, which I don't think support holds in that same sense.
It will bill your 4 EUR (on a tram/bus) or the whole 20 (or something on a train) instead of the actual journey price if you forget to checkout. Pretty sure it can decline cards for insufficient balance too. Not sure the entry gate blocks the amount.
Actual chipcards don't bill you at the end of the month either -- they reload a fixed amount through direct debit (which takes a few days) the moment your balance crosses zero. If the direct debit isn't setup for a card (because it's not a personalized card) or the debit was rejected, the card is blocked.
For business chipcards cards it works somewhat the way you described.
It definitely exists in Amsterdam, no? When I visit I just tap my card/phone on NFC enabled card checking machines (which exist in and out of the stations)
It also wouldn't work as you describe, as the terminal at the point of entry doesn't know how much to charge you since it doesn't know where your journey ends.