I make deposits at the counter for the business takings, and I often add it up wrong because I'm in a hurry or I'm just dumb.
It's amazing how little cash there is these days compared to 15 years ago....another thread I suppose.
Anyway, one time in about 1995 I made a deposit over the counter, and the teller put all the $20 notes into a note weighing/counting machine. You could see it from the counter, doing it's thing; very clever device.
The amount was $20 short from what I had added it up to be. I thought it was odd, but thought maybe I'd counted it wrong, and accepted what she said.
About an hour later, I got a call at the shop from the bank. Apologising for the mistake in my deposit - the machine had counted the money wrong, and I had been credited a further $20. She had gone to use the machine a bit later and had found the note stuck in the machine.
With the ATM situation; I'm with you on this, even though I have done it, and so far had no problem with it.
How would you go if there was a mistake? It's your word against theirs; even if you have counted it 5 times before the deposit is made?
Watching them count at the counter is still the best way.