Sounds like the US and Euro systems work fine within their own borders. Solutions designed for one make less sense in the context of the other.
If you tried to make a purchase above the spending limit it was a hassle. I am old tho.
By the way, here banks even have daily bank / wire transfer limit that can be changed only by a personal visit to a branch, so even if your online banking credentials are stolen, the attacker can not empty your account.
And that doesn’t always work. For example, at a Chevron petrol station in California in the middle of nowhere we tried several European credit and debit cards, and nothing worked. At the end, the guy working there helped us with some prepaid option at the counter. He didn’t believe us until he tried himself that really none of our cards worked.
But the situation is way better than 5+ years ago. Back then, almost every second purchase of ours had some problem with our cards in the US. Now, we had like one or two in more than a week.
But of course, some car rental companies still pretend that they are generous that they allow debit cards. Not just in the US.
The "credit" button in the US really means "use the Visa/Mastercard network and don't ask me for a PIN", as opposed to "feel free to ask me for my PIN and route the transaction over one of a dozen or so US domestic debit networks". The question doesn't even make sense for non-US debit cards.