I think Chase starts “Private Client” at $250 or $300k. (Don’t use Chase, however.)
It might in some cases be more trouble than it is worth, if you are right around the threshold. A “normal” retail checking account and a brokerage account at another institution with the ability to transfer between them is probably sufficient for most. If you need loans or mortgages or other stuff, it might be worth the hassle (and phone calls).
(Not trying to diminish private client services. But they’re night and day different services.)
That sounds high to me. Maybe American banks? The smaller Swiss banks will start taking your calls at about $2m.
The non retail banks that have a good reputation are even higher.
They don’t outwardly advertise their minimums because “it depends.” For example if you’re an up and comer in your field where it seems like you’re LIKELY to one day hit the mins, they’ll start the relationship early.
They also invite you to all the bank's private events, so you can schmooze with other high net worth people. Banks are always sponsoring fancy events everywhere, and private banking clients generally get free invites.