You are correct. Banks have many mechanisms for sending money from A to B, on the low end there’s Zelle, then there’s free inter bank transfers, then good old wire transfers (unlimited amounts, usually cost $25).

I send electronic payments all the time, just not payments big enough to exceed maximum transfer limits. For example, Coinbase might say max transfer for ACH of 5000 USD per day, for larger deposits use a wire transfer. I’ve never done the type of transfer that exceeds the maximum ACH limit.