Cash & digital can be complementary.
One post office trip per quarter: one money order per vendor, one batch of envelopes mailed.
Monthly online bills will have a negative balance to indicate the credit.
Zero data leaked to payment middlemen.
In the United States you can.
Almost all bills, utility and otherwise, can be paid for in cash at most supermarkets or other money-handling businesses. ("Currency exchanges" in Chicago, or whatever your local equivalent is.)
Also, every utility company I've had serving my last five apartments has had a public lobby where people can make cash payments. I suspect even cell phone bills can be paid with cash at a cell phone company's retail store.
So long as you are on a post-paid account you don't even need this. If you are on a post-paid plan of any sort, it's a debt. You have the legal right (via the Coinage Act) to pay that debt via cash regardless of any systems they might not have setup to do so.
It's a fun game to play sometimes to remind institutions of this fact, and usually rouses some bored corporate counsel from their slumber to first argue with you, then apologize.
Probably doesn't really help build a great business relationship, however.