Far too many wrong assumptions in this thread!
It's a design limitation of the Intel 945 chipset. Any computer with the same chipset is similarly afflicted. The iMac 5,1 would have shipped with 512MB which was plenty at the time. The 965 fixed the issue a year later in the aluminium iMacs.
The Core 2 Duo is 64-bit capable as is OS X on compatible hardware, including the old PowerPC G5. That said, Apple boot most pre-2009 Intel machines in EFI32 mode. Core 2 machines will run 64-bit Intel applications on OS X 10.5 and higher no problem even on the older hardware.