The Neo Geo doesn't have a way to directly output analog or digital video from the cartridge slot, it is impossible for the Neo Geo to be a "dumb terminal" and act as just a power and AV source for a system-on-a-chip in a cartridge. Whoever told you NG DEV games do that is a moron.
The only reason they went with "all that processing power" is those chips are still being manufactured and are therefore inexpensive. Why would they pay more for a less powerful solution to their needs? Given what we know about the Neo Geo hardware (see
http://wiki.neogeodev.org), it's safe to say the FPGA and CPLD chips in NG DEV cartridges is just for data mapping, decompression, decryption, demultiplexing and/or anti-piracy protection.