a 16 bit CPU, in this case, say the 65816, is already faster than the 65c02, and has access to all of it's modes and them some. 16 bit mathery is going to benefit from a 16 bit CPU. You can do shit half as fast basically. What you describe (8 bit CPU with 16 bit addressing modes) is basically a z80. Indirect indexed on the 6502 is 16 bit apparently. But f*ck that crap.
Both absolute and indirect addressing modes on the 65x are 16bit. 16bit addressing wasn't a stranger to 8bit cpu, it was the norm. If you mean indexing, then yeah - only 8bit. The 6809 cpu has 16bit indexing though.
The 65816 is a kind of crap cpu though. For two reasons: it was originally made pin compatible with the 6502 and thus 24bit addressing is done through multiplexing the data bus and address bus - you have to use an external register to latch this (using Phase 1 and Phase 2) . This means all roms have to be twice as fast in the cpu clock rate. A 20mhz 65816 would need 40mhz memory. That's really shitty. Even on the snes with it's custom package, those rom speed requirements are still there (that's why there's a option to run the cpu in slower speed, slower speed roms were cheaper). A 7.16mhz 65816 on the SGX would require ~50ns rom (as well as ram) or introduce wait states which would defeat the purpose. Second, the 8bit data bus is pathetic. It hinders the real power of that processor design. It would be incredibly fast if the data bus was 16bit (it's gimped similar to the 68008 8bit data bus 68k, although not as bad). The 65816 is also missing some opcodes from the 65C02 (there are two official revisions of this processor, the second one adds more opcodes - and is what the 6280 version is based off of), so it's only backwards compatible with the 6502, not the 65C02 or 65C02S. And all the 6280 opcode slots are already taken up on the 65816.
I don't think it's worth having a 16bit cpu (ala 65816) in the SGX if it means breaking compatibility with the PCE. An external DMA controller to take the load off cpu for graphic updates would do good for the system (16bit DMA writes to the VDC for twice the transfer rate as the Txx). The 6280 has a few opcode slots open for upgrades, they could have added additional register (16bit indexing), address to address 16bit math (macro instructions), long 24bit addressing, and such through these. Even chain or paired opcodes, like the z80 prefix opcodes (there have been external hardware upgrades to the original 6502 that did stuff like this). If not done on the processor, it could have been handled via an external controller unit (like the SNES does or the Arcade Card on the PCE); 24bit addressing with self incrementing or decrementing, etc. There's plenty of open bus area in the hardware bank ($ff) for this (it's what the arcade card does).
I bought the SGX back in early '93 and was a little disappointed that they did nothing to upgrade the sound. It still had the same thin/skinny bottom end as the PCE. Two additional DMA DAC channels would have cleared that up. I would take that sort of upgrade over any cpu upgrade.