There are other tipping cultures outside the USA, you know? Tipping is very common in the Balkans and other countries that were influenced by Ottoman culture, for example. While it is not expected, many coffee shops all around Europe also have tipping jars.
It's really not common in much of Europe at least for people to actually discourage tipping (though they may seek to refuse what they perceive as exorbitant tips).
I have lived in Istanbul for a decade now and while many of us do tip, and tipping is rarely expected. The expectation is higher than foreigners, but if you live here, you end up eating at the same places over and over, and that expectation goes away fairly quickly. When I first moved here I realized I was tipping 3-5x what a local would, because I was tipping American standard.
Tipping is mostly expected when there is a lot of service involved in the meal. This means either fine-dining, or Meyhanes where you spend 3-5 hours drinking heavily (Raki/Ouzo) and eating mezes & fish.
I think the tipping culture you're talking about is "Bakshish" which is really more of a bribe than a tip. It doesn't exist much in Turkiye anymore (unless you're an Arab or Syrian refugee, their experience is far different than others).
Bakshish is still very prevalent throughout the lower Balkans, Serbia and most Islamic nations I've visited and worked in, except for KSA and UAE (they'll kill you for that shit.)
I haven't been to Turkey, so I don't know how the culture evolved there. However, in former Ottoman-controlled states that I've been to (and especially in Romania, where I was born and live), tipping (as well as small bribes, which are both called bacșiș here, same word as bakshish, though that is changing somewhat recently) is quite prevalent and expected in many settings. At the very least, in any setting where you are served by someone while sitting down, even if it's just drinks at a bar, you are expected to tip (typically 10% being seen as a tip for cases where you were happy with the service).
Tip jars are perhaps a more recent phenomenon, but they are now almost ubiquitous in all places that serve anything, event at a counter or to go - including club bars, coffee shops, even many fast food places.
Definitely more of a bribe, and common in a lot of the world, in the countries mentioned but plenty of others, esp. the African ones I worked in; different names but same idea.
A "cost of doing business, and we appreciate the opportunity" gesture. Prove that you're serious, and that you want an actual result.
There are a lot of business dark patterns, and when they are prevalent in that society, that society is always poor and corrupt.
An Egyptian friend, once warned his friends about me: "Now he's American. When he says 2pm he means 2pm, and when he says we have to leave at 8, that means we have to leave at 8. This is why Americans are rich. They respect schedules, and care more abut business than friends or family."
I was just going to say - from Croatia - in most of my circles if you don't leave a 10% tip you're either poor or a miser. Frankly even if you're poor, you likely won't go rather than count cents - only relatives in retirement don't leave tips when they insist on paying.
You're not legally obliged to give it - but it's very much expected and you can see the awkwardness when you skip it.
Like just the other month I was in this resort with my family and first night we checked in we went for diner - waiter was very polite, entertained my one year old and gave us tips about the area. We didn't have cash on us so we put it on the room and signed the receipt. Next day he was still professional but not as much effort - then I left a tip for both dinners and suddenly it's back to chat mode, how was your stay, parting drink on the house, please do come back, etc.
In coffee shops you can see the looks you get when you wait for small change.
The problem with US is that it's so culturaly ingrained that it's really not optional anymore, even if it technically is and no one will call the police on you for not doing it.
As a personal anecdote - when I visited America on a business trip we went to a restaurant where the staff was literally rude to us, the food order was not what we ordered and massively late, and yet our hosts insisted on leaving a 10% tip because
1) low tip will show them they have done a poor job(?!?!?!?!?!)
2) we would look like jerks for not tipping(their explanation).
So basically my takeaway is - if you have to tip even when your experience is poor, or you risk "looking like a jerk", then it's not really optional.
But that's what tipping is here too - it's basically signaling you're not a miser. Sure it's supposed to encourage better service but that's secondary. Just like buying rounds, etc.
Sure, but the OP's cafe literally doesn't allow tipping, it's not that they don't expect them. That's what's bizarre/noteworthy on this front - and it's definitely not how every coffeeshop in the rest of the world operates.
It's really not common in much of Europe at least for people to actually discourage tipping (though they may seek to refuse what they perceive as exorbitant tips).