It does make sense. Most big companies pay a week in arrears, so they have time to prepare the payroll and send the DD orders. They did this even before DD was popular so they'd have time to get the payroll right. In the bad old days they had to calculate each paycheck manually and post it to ledgers manually. Even for a larger small company, this could take days.

As an employer, you must communicate the pay period and payroll schedule to your employees. Usually this is part of the employee handbook. For your case, it'd be something like "The work week and the weekly pay period is from Monday - Sunday. Payroll is paid on the following Friday."  You could actually make it Wednesday, if you can reliably get the payroll done and sent on Monday before 5pm. But you have to get it done. Depending on how complicated your payroll is, that may be rather aggressive.

Once the pay period and related pay dates are communicated then you're expected to make payroll, at all cost, on each payroll date. The rule is the employees have to have their money on the payroll date, whether that be a paper check or a direct deposit arriving in their bank account.

There's nothing wrong with paying in arrears, at least up to a full week. Every employer I've worked for since college paid me on the Friday after the pay period ended.

What isn't compliant with the DOL is paying the employees late ("holding payroll") for any reason, compared to the payroll date communicated ahead of time. Allowances are made for unexpected issues, such as computer or power failures or bank screw-ups, but your internal processes should be set up so that you can regularly make payroll.  "I was sick or tired or too busy" aren't reasons to miss payroll.  "I don't have the money for a couple of days" is possibly the worst reason you could ever give your employees to be late.

Interestingly, you also aren't compliant if you give your employees their live paper paycheck early, before the payroll date, a check that is dated in the future, and you ask them to sit on it until payday.  I'm not sure what employer abuse that's designed to solve for, but it is a rule.

If you're open 7 days a week, you can technically set your payroll date on any day of the week you want. As long as its regular so the employees understand when they'll be paid and you're there to hand out paychecks. However, when DD is involved, then the payroll date has to be a banking day, so then weekends are out.