1) Some raids take PCs while they're still on, in order to preserve things like encryption keys in memory or cached passwords. It's possible to transfer a running PC over to a battery-powered outlet for transport, then to lab power for analysis. This would be very useful if the machine was using full-disk encryption.
2) Having a full disk image gives you the data, but the easiest way to see how the data behaves is to actually boot up the machine (after imaging the drives, obviously) and see it as the suspect would. There might be subtle differences in behavior if you use lab hardware rather than the actual hardware, and there's even a chance of something crazy like the suspect using a modified Linux kernel that wipes his drives if it detects different hardware.
3) It's a pain in the ass to remove hard drives in some guy's living room when you can just haul the whole thing back to the lab and do it there. I suspect that laziness generally wins over the inconvenience to a potential suspect.