There is, it's called debit cards, but Stripe et al. "simplified" pricing by charging a percentage regardless of card type instead of the traditional interchange-plus pricing. Merchant banks "used to" make money by tacking on fixed fees, i.e. a set-up fee, terminal fee, monthly fee, etc, but then Stripe came along and provided (1) a better dev experience, (2) better onboarding, and (3) simplified pricing.
Debit cards still go through the same credit card infrastructure. The practical difference at this point is whether the card company backend defer payment until collection date for the benefit of customers, or don't wait and just call APIs on the spot. There's a whole "internet" of credit card infra that lets you pay using those numbers on the card like they are phone numbers.
Stripe don't do handle their own payment, they just wrap someone else's API, and pay them in percentages and dollars per API calls(idk about the ones behind Stripe, but I think I saw somewhere that those middlemen often charge both? Egregious, but they're literally old boys money men and they have lots of leverages against you).
What are truly different to credit/debit card systems are things like PayPal, Apple/Google and such gift cards with scratch areas, and Chinese QR payment apps. Those are the ones that don't (always) go through the CC ecosystem.
Debit cards aren't that, in practice, because as you say they typically get the same 3% fee whenever I've asked. Toast and other point of sale networks just charge it based on the network and not the card type.
But even so, I still prefer the credit card instrument, used as a "charge card". For those that don't know, a "charge card" is common with businesses and is expected to be paid off every month. But it helps with managing your cashflow - e.g. you can keep your money in a savings account all month and make one transaction at the end - and it keeps your actual money from being at risk of fraud.
Most Europeans seem confused with how Americans use credit cards for everything, but about half of us use them as charge cards, paying them off every month.
That is a benefit, so I can see paying a small percentage for it, but I don't think that benefit alone justifies the 3-5% of a transaction that credit cards charge now.
Most stripe transactions do use cost-plus pricing. The flat pricing is popular with smaller businesses, but larger companies graduate from it pretty quickly.
Also debit cards run by smaller credit unions charge credit-card like fees (and then are used by fintechs to earn fees while making it harder to pass those fees on to end users).
You have to wait for the investigation to complete to receive compensation if you’re hit by fraud on a debit card. Credit cards don’t share that issue. If you’re poor or living paycheck-to-paycheck, debit cards are potentially a risk to your livelihood.
Fun fact: Visa owns some of Stripe.
For US readers - in my country in europe I'd say that 95% of people have only debit card, not credit card. it's very not common to have a credit card here. Card payments are extremely common, but everyone uses debit card.