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On a long enough timeline everything and everyone can be compromised (or the institution fails before then)

Exactly - either the data is basically not valuable at all (the category for which PII rarely fits) or else when the company collapses or is bought, the data moves too.

There's always an incentive to steal or leak it to other companies for money; so as long as the incentives are aligned with GATHER ALL DATA and KEEP IT FOREVER then yes, it will just be a matter of a time before each data store is compromised by mistake or purposefully.

I doubt the claim, but the sentiment I think is valid. If you think about what data these entities are holding, it's not unique to a single database or entity. Your name/address/phone/ssn/etc. Is likely stored in so many places that the probability it gets leaked from at least one eventually I'd say is very nearly, if not 100%.

Why on earth did you pick this username