what @girevik is saying is that no amount of buying can create a global fiat run but if everyone customer at "Alice bank" buys bitcoin using an exchange that banks with "Bob bank" then "Alice bank" can definitely have a run and "bob bank" will be left standing.
same amount of fiat in the system just all at a new bank
"Alice bank" collapses and "Bob Bank" is bigger
today "Bob Bank" is JPMorgan and will be the last bank standing and will soon be called JPMorgan-Fed bank
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