As much of a believer as I am of Bitcoin, I'd say the chances of a bank run happening because of crypto is very slim. Crypto is gaining popularity, but it's still very small in the grand scheme of things, and it's still more widely treated as a speculative asset and an investment vehicle rather than an actual alternative to fiat. I'd like to believe things are changing on that end, but it's coming on extremely slowly. Moreover, cryptos need to scale first and foremost, before we can talk about it being a viable replacement.
All in all, crypto certainly does have the potential to disrupt banking and fiat, but it's still way far off from reaching that potential. Governments/banks aren't afraid of it in its current incarnation -- they're afraid of its potential.
Yes, you are right... today. But, as crypto gains popularity, it gains more adoption. As it gains more adoption, it gains more popularity and awareness. At some point, there is going to be a tipping point - when we hit critical mass. At THAT point, this is why things will accelerate very quickly.
Think about the Internet itself. It had been around for years before it gain true adoption... then came along a little company called Prodigy. That helped mass adoption... but adoption really happened when AOL launched it's killer app AOL Instant messager. Then things blew up. Everyone NEEDED the internet. The snowball affect kicked in and the rest is history.
... same thing will happen to crypto as UI/UX interfaces get better, as merchant adoption becomes easier, etc. It's only to take one killer app that everyone wants to use to quickly accelerate things.
Even now some folks ask... why do we need crypto? Well, back in 1990 I could have said the same thing about the Internet (and many folks did). The truth is, that we don't need crypto. We don't need the internet.... but dang we love it and it can you imagine life without it at this point!!!???
When the digital run on the banks happen, the dollar will naturally hyerpinflate to the price of crypto. To buy crypto, it will be very expensive and those who want to 'use' it, will be left behind and will realize that their precious fiat has been naturally devalued as crypto becomes a more dominant way to spend money.
Cheers!