The need to keep around the old hardware depends on your goals. If you're into historical preservation, then you of course would keep, restore, and maintain an old machine. If you just want to move the data and programs and exit the platform, then donate the hardware to someone who wants to use it.
I've written an emulator program that emulates an Altair 8800. Functional? Yes. Does it run old programs? Yes. Fun to use? I think so, if you like ASCII character-based games. Is it the same to operate as the real one? No, not exactly.
Once you've moved your data and programs from the old machine to the emulated machine, you don't really need the old machine. Yes, some formats are easier to move than others and don't require the original hardware, but others can't be read by modern PCs without rediculous amounts of effort. So, you use the old machine to continue to move programs to another media so that the bits can be preserved.
But, there are reasons to keep the old machine. First, it's the overall feel of operating the machine in person. Second, some programs and games just plain feel better on the original hardware. Thrid, it's preservation of computing history. Fourth, there's no better way to understand how a system works than to physically work on it. I want my kids to sit at my first computer, a VIC-20, and play the same games I played as a kid.
Along these lines, I set up an Atari 2600 along side of the Nintendo. Believe it or not, they play the 2600 as much or more than the Nintendo. Although the graphics are nothing in comparison, the games are engaging so they keep coming back.
I didn't appreciate the difference between an emulation and the real thing until I got my own Altair. There's no substitute for clicking the switches yourself, for swapping around boards, or for running tape through a paper tape reader.