It would be difficult to just blindly sample at a fixed clock rate using the FX2LP. Because the ADC clock is not synchronous to the FX2LP's clock, a situation where the FX2LP samples at an edge (which causes metastability) could occur. The FPGA is able to fix this issue by sampling the ADC clock at 60 MHz, and then detecting edges, allowing it to figure out when the ADC data being output is valid. The FX2LP, which just blindly samples at 24 MHz, can't do that.
Here's an example of what could happen if you just blindly sample the ADC output at 24 MHz. The orange arrows are when the FX2LP samples. The black line is the ADC clock and the green represents the data. When the FX2LP samples on the falling edge of the ADC clock, the data may not have settled yet. In my example this is shown by the FX2LP reading 0x04 instead of 0x00 on the transition (since perhaps the 3rd bit is slower than the other bits). This would lead to bad samples showing up in the data. There is no easy way to detect such a situation too, since reading the clock wouldn't work. At the edge, the value the FX2LP reads is undefined, and it could be either 0 or 1.