Well actually no most banks globally don't. The majority of the western world is moving away from cheque accounts due to fraud, and more efficient payment systems.
Case-in-point, in Australia, the major tier 1 & 2 banks got together to collectively outsource their cheque operations due to the decline in revenues but not operating costs. They realized that within the next 10 years cheque accounts will be virtually non-existent, and wanted to get the costs off their books ASAP and focus on more profitable payment systems i.e. GIRO, BPAY, etc.
The cheque processing systems today but still don't actually check the dates and this left up to the teller - now we are back to people again. Posted dated or not, once the cheque has been processed the funds are coming out of your account. Your only saving grace is the imaging systems that scan the cheques for archiving purposes before processing, this way the banks can quickly pull up your presented cheque for confirmation.
Paranoid, certainly why wouldn't you be when it’s your money, or where you born with a silver spoon in your mouth and your mummy and daddy didn't teach you the value of money!