Yes, there is certainly much more to be said, but that's beyond the scope here.
At the point you are able to communicate via I2C/SPI at X Mbit/s rate, you should certainly be able to communicate via parallel interface at X MByte/s rate, which is cca. one order of magnitude higher speed. Of course at the cost of increased pin numbers, board space and I-don't-know-what-else.
But at that point one would ask: why would you want to transfer X MBytes/s, your mcu would do nothing else than dump the data in and/or out? Well, technically yes, but that's the wrong question. The right question is, do I need that transfer speed? If yes, let me have it.

Each tool has its application and each task has the right tool(s) to solve it. It is good to have a deskful of tools around, or at least to know where to get them, just for the case.

Jan Waclawek

ps. Erik, good point with the interrupt line parallel to I2C/whatever, an another one which should be made a FAQ