> The above is a gross oversimplification, but I don't think its wrong in that
That does seem like a gross oversimplification.
First and foremost, I'd say that there is nothing inherently unique about recourse when a bank goes bankrupt. It's merely based on conventions and contracts. How that works is that there's an insurance corporation, the federal deposit insurance corporation, which insures deposits at banks up to $250k. That's all. Of course, this isn't free. It's costing all of us money, as any insurance does.
What this means is that you can build any type of system and throw an insurance product on top and it'd be no different. There's nothing unique about FDIC.
Of course, we must realize also that FDIC insurance only covers about 1%, at most 2%, of deposits. So it's only really effective when a few banks go bankrupt. A complete systemic meltdown that we were very close to would've made FDIC useless. Fact is, the only reason that didn't happen is because we magically created a trillion dollars out of thin air to create magic demand for toxic assets nobody wanted and were causing imminent bankruptcies. And that, too, comes with a price to ordinary citizens. Nothing special about it, and it's certainly costing us all money.
As for Paypal? It's regulated to death. In some places it's regulated like a bank. In other places it's regulated as a money transmitter, as a money services business, as a non-bank financial institution. All of those carry real regulatory obligations. For example, there's a law where a money services business can't do fractional reserve, i.e. you're by law required to keep 100% of your custodial funds (funds from customers that you hold). There's another requirement that requires you to separate company funds from custodial funds, meaning if your company goes bankrupt, the customer funds are untouched. As for Paypal simply 'taking your money', that's illegal, and you have legal recourse. That may not be perfect, I'm not saying it is, but it's similarly imperfect as when the police seize your funds. In both case you have legal resource, Paypal is not unique in being above the law.
And then lastly, there's surety bonds. So in virtually every state Paypal operates, it needs to hold sufficient surety bonds. That means, literally, insurance. They pay every year some company which insures them, so that if say they go bankrupt or flee the country, this company has a surety bond for the customers to get paid out.
And lastly, a non-legal point, but just a practical one: Paypal is worth a lot of money, the 150m users are worth a lot of money. That doesn't mean they can't go bankrupt, but unless they're knee-deep into complex derivatives they don't understand, like banks the past decade, I'd say the chances of them disappearing with everyone's money is pretty slim. Not saying it won't happen, just saying it wouldn't be a reason for me not ever use Paypal.