I assume when you say cooling elements you are refering to the evaporator coil on the back wall of your freezer? If that is the case then yes your repairman is correct, you should have NO ice on that coil . What you should have is a small amount of frost on the entire coil from top to bottom, if that coil is only partially frosted as you indicate that would mean your system is low on refrigerant. If it is low on refrigerant, that would mean you have a leak in the system somewhere. That leak would have to be repaired before it can be recharged, all this equal big bucks.