That's not true. These days even the smallest US banks tend to have mobile apps or normal mobile banking options. All the major banks without exception do. That has been true for years at this point.

Deposits, moving money in various ways, checking balances or statements, bill pay, customer service, etc etc. What exactly is missing that is important that American banking desperately lacks? The larger banks are borderline obnoxious with the options ('features') they try push on you, for what their mobile banking offers now.

The only thing I can think of, is easy & instant account funds transfer from one person's bank account to another person's bank account (which is a structural flaw in the US system, and which PayPal & Co. fill).