You're giving Paypal and Robinhood too much credit. It wouldn't surprise anyone if they both consider themselves "too big to fail" and do not have sufficient crypto to cover themselves. It's easy to imagine the meetings where someone "important" says "That will never happen, end of discussion." and then it turns out they they're wrong and they get bailed out (or not).
These meetings don't exist. Occasionally fraud and negligence happens, but not this casually. People running PayPal-sized companies are neither completely stupid not completely evil. A bit yes, but not this much.
"Too big to fail" - and that's how you increase the supply of BTC without actually doing so I think.
As long as an entity (such as the government) prints money and takes the hit on the spread people will see contracts of BTC as equivalent as BTC w.r.t value. Its basically banking, but since fiat is still the prime currency of legal settlement (not BTC) no one will think its possible to "run the bank" as that entity in the event of a run will pay the difference. BTC is not actually required to settle anything by most countries laws, so actually delivery of BTC isn't guaranteed. This does undermine actual BTC especially if actual BTC is harder to spend - the pseduo-BTC would then have more utility.
In other words BTC could be the same as fiat potentially in the longer term. It will be more transparent of course since it it easier to take delivery of than say gold (or cash but less so), but as long as they don't give you that option in your product that's fine. Even cash is like this with withdrawal limits, and other laws. If fiat was only valued by the actual cash in the economy it would be worth a lot more than it is now btw.
