It isn't "active" or "inactive". You are just shutting off the throughput so it doesn't re-record what is in the room when you are recording vocals. You shut the room monitors off and use headphones when you do your singing so the mic does't record the room sound behind the vocals onto the vocal tracks, right?

As far as the unplugging part, seriously, is the .7 seconds it takes to plug or unplug a mic cable going to set your productivity back a whole lot? I do unplug mine but that's because I switch between different mics for different things.

All personal preference here like so many things are. Things like this are often determined by other conditions, like how you interface to your computer. I have a mic preamp that has 2 inputs and 2 outputs, so I can leave 2 mics plugged in if I choose to. I also use a patch bay and just use a patch cord to configure what goes to the M-Audio that way. But that's just what I have and not everybody has the same stuff. Some of the guys have mic preamps with 8 inputs, thus can have up to 8 mics connected at all times.

The beauty of creativity!!! Many ways to the destination.