Really?!? Sounds more like the plot of a good thriller movie. While it is theoretically possible to put explosives in a coat lining, the amount of the explosives is somewhat limited, and at the end of the day it is stored in a closed area, so any explosion will likely be limited and contained to some degree. No security system can reduce the risk to zero. The reason why you can't leave a car or a package unattended is because they are in more open areas. In the case of the car, it could have significant explosives on-board and an unattended package can contain a shrapnel bomb. So if they go off, particularly with some type of shrapnel inside, they can cause significant damage to either structures or people, or both.
While keeping the pre-security areas of the airport safe is part of the mandate, it is not the primary concern. Someone who is that determined could just as easily put that coat or a paper bag containing explosives into any garbage can and it would likely not be detected, so not having a coat check does not solve the problem. The primary objective of airport security is to keep the aircraft and passengers safe, so that a repeat of 9/11 is prevented. What happens pre-security is secondary. Hardly a reason not to have coat checks!