I am not expressing any opinion on the merits of the bank's legal position here.
But as a practical matter, do you want to have to file a lawsuit over a fairly small amount of cash?
I don't want to do that, so I don't deal with bank machines, because I am aware this is something banks do very often, and I don't want to deal with it. I am not just spouting paranoid fear here. Banks actually do this all the time. If that's something you want to deal with, more power to you.
Of course, the reverse can happen too. I had a friend who got $80 when he asked for $20 (i.e. his account was debited for $20 but he got $80 in cash). So maybe over your lifetime, the various problems with the machine will average out. But I just prefer to remove this potential source of stress from my life.
Unless you cite me actual statistics on how often this occurs (not just your or a series of anecdotes), I see no reason to change my behavior (or more generally, why anybody should change their behavior) based on an error that can occur.
Errors occur with any system you use. That's guaranteed. If I'm going to avoid using a system because of possible errors, I want to know what error rate we're dealing with. If it's one in say 10,000 cash deposits, I don't mind taking that risk considering I have to go out of my way to a branch with a human teller as opposed to an ATM. This is especially true considering that I, and I assume most people, rarely do cash deposits these days. For people who do cash deposits on a regular basis, it's more of a concern, but again, it all depends on the actual error rate.
Also, the receipt is irrelevant -- you may be misunderstanding what I am saying. The receipt is evidence that the machine believes you put in a certain amount. It's not evidence that you actually put in that amount, which is what the bank is disputing.
The receipt is absolutely relevant. You seem convinced that some banks, whether maliciously or just out of error, want to "tamper" with your deposit amount after you've made the deposit. The receipt is the only evidence that you have that the bank can't tamper with that you can present to dispute the bank if need be.