If they had mailed the payment on April 15 to some place on the Ohio River, they would not have been delivered yet and it might take the private bank a couple more days to process them.  The 1040-ES instructions tell us,

If you mail your payment and it is postmarked by the
due date, the date of the U.S. postmark is considered the
date of payment. 

Does anyone really think that the banks are keeping copies of the envelopes with postmarks?  This is 1950s outlook on tax administration, left from back when all 58 district offices processed returns and payments and April 16 was celebrated by IRS employees as "Opening Day."

The instructions also remind us, "You can pay all of your estimated tax by April 15, 2021, or in four equal amounts by the dates shown below."  In these days of low interest rates, I have several clients who prefer to do that.  I don't wear suspenders and a green eye shade and I don't babysit my clients who could pay their tax through withholding but don't.  However, It's OK with me if other practitioners want to provide that service. 

Their job, though, should be to lower expectations, not to overpromise.  "You know, nothing set up online with IRS computers is fail-safe these days, so we'll do this but it's a good idea to check your statements at the end of the month and make sure the money came out of your account.  And if it doesn't, it's no big deal.  Just go back to the way most other people choose. It's not really a deadline, it's a squishy due date."

Sort of like paper returns -- IRS doesn't start checking postmarks until a week or so after April 15.  

Yes, I know.  Not all of the lockboxes are on the Ohio River and might have to close if it floods.  We have one in hurricane country, where Hugo knocked out power for weeks, back in 1989.  So electronic payments are the way to go.  Teach a client how to do it and they may start paying all their bills that way.