If you're worried the hard drives won't spin back up, I'd say you should instead spin them down regularly so you know that risk is basically zero. If you're worried the power supply will explode and surge into the drives when you turn it on, you should not be using that power supply at all. Any other risks to powering it down?

And for the particular issue of replacing a failed drive and not wanting to open up the case while it's powered, you can get a single drive USB enclosure to "hot swap" for $20. And if you use hard drives you should already have one of those laying around, imo.