There are higher limit ATMs and accounts. Some Chase and Citibank accounts go up to $5000 iirc.

Usually there’s a “rich people” account with different limits and services. I knew somebody once who could call their guy have money delivered by courier in NYC.

If you're changing money, you don't have to be a rich person to get money by courier if you have a Citibank account.

Citi's World Wallet program delivers money by courier or FedEx, depending on where in the world you happen to be when you order.

At least it did before COVID. Considering how Citi has cut branches and services since 2019, it might be different now.

I don't know about $2K but I definitely had a $1K limit on one of my ATM cards at one point.