If you have the parts in your hand (not soldered into an operating circuit), the Raspberry PI is pretty compelling. You can send commands, retrieve data, store the data or format and print the data.
Otherwise, you need to go to the datasheet for the various devices to see how fast they might run and then buy test equipment of sufficient capability. I suspect a logic analyzer will need to run at 100 MHz or so but I'm just guessing. Furthermore, where would the LA store several GB of memory? That's why the PI is so useful. It has a filesystem, it can read at whatever rate is convenient (Python scripts for I2C and SPI, I don't know how I would do eMMC at the moment) and store endless amounts of data either to the onboard filesystem or to an networked file server with TBs of storage.