I used to work for Navy Federal Credit Union and got to observe a LOT of the day to day operations.
The way a large financial institution handles checks is absolutely incredible.
I would say that in 99.999% of all cases, human hands never even touch the check.
Machines open the envelopes, extract the payment stub (if a payment) and the payment check, scanners orient both properly (including flipping them over if they're backwards), and imaging them.
What a lot of people don't know is that the ink used to print the account and routing transit numbers at the bottom of the check (as well as some other numbers on the check) are not only machine readable, they're also magnetic. It's an anti-forgery mechanism, but it also helps make automation faster and more sure.
Back in 1996 on any given day Navy Federal was getting in 100,000 or more checks for various payments.