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.