There was a long time when Stripe was taking a significantly higher transaction fee than most other merchants for cc transactions yet there still was fervent developer push to use it anyways (Note, this hasn't been true for a few years and was only true during the first year or two of Stripe's life).
People made all kinds of rationalizations to themselves for using stripe at a much higher cost simply because they didn't want to spend a couple more hours using crappier API's or digging through crappier API documentation.
It made no sense to me at the time because while Stripe was nice, it was usually only a matter of a couple hours/days to implement any of the other big payment processors of the time. I guess that shows what the power of cultish developer zeitgeist can do.
My first business that used Stripe was with them from their early days in the UK, and my recollection is very different to yours. They were potentially a bit more expensive in terms of fees than getting a separate merchant account and payment gateway set up, but not hugely so and at least they were consistent and transparent about those fees.
Moreover, they were vastly different in terms of the ease of integration. To take card payments via the traditional big banks and other established services, you didn't just have to put up with awful APIs and worse documentation, you also had to put up with onerous application processes that could take days to collect the required information to apply, then weeks to approve (or not), and even then often imposed severe restrictions for businesses with no trading history up to and including piercing agreements for company officers, large and long-lasting reserves being withheld, etc. The only other game in town for setting up online card payments reasonably quickly and easily at that time was PayPal, which had a reputation somewhere between Satan and the devil even then.
Of course none of this is unique today, and there are now many other services available for taking payments via card or many other methods. But in those days, it truly was a game-changer. As much as I criticise Stripe for its more recent failures, I also give credit where it's due: many small businesses, including at least one of my own, would not have gotten off the ground as early as they did without Stripe.
U.K. was probably different, but in my mind both Authorize.net and PayPal were the established players in the US market for online credit card transactions before Stripe.
Authorize.net was (and still is) a "gateway" - you pick the merchant and use Authorize.net for the actual technical layer of processing a transaction - which was kind of a confusing concept, but there were plenty of merchants on authorize.net's marketplace that had much better rates than Stripe. I don't recall there being an onerous application process or the restrictions you mentioned, but it could be that I was shielded from that side of things.
Both Authorize.net and PayPal had pretty gross API's (and documentation) but they were pretty solid once you got them working. Obviously it depends on the nature of your business, but saving even 10 cents per transactions goes a long ways for many and quickly justifies a day or even a week of additional coder time. It wasn't that onerous of a task to implement one of the non-Stripe options.
Paypal of course was it's own beast with it's insanely draconian policies towards account holders, but I never had to deal with that (luckily).
I am sure many developers don't remember just how much crappier the "crappier APIs" were. Back when Stripe became popular the alternative was XML and SOAP, documented in an outdated PDF that would get emailed to you, or if you're lucky, hosted behind 3 login walls. Then, once you start integrating, you realize that their dev environment is offline every other request, and doesn't match the production environment. So you just do the work blindly and hope for the best.
Having a decent publicly documented API was revolutionary.
People made all kinds of rationalizations to themselves for using stripe at a much higher cost simply because they didn't want to spend a couple more hours using crappier API's or digging through crappier API documentation.
It made no sense to me at the time because while Stripe was nice, it was usually only a matter of a couple hours/days to implement any of the other big payment processors of the time. I guess that shows what the power of cultish developer zeitgeist can do.