Leave the turntable running?

I do it all the time. No problems. YMMV.

Yes it means being able to grab the record edges and lifting it in one smooth motion.The Rega, using a glass platter and a felt mat, makes this easy. (the only flaw is if the Lp is really static'y, then the felt mat sticks to the LP. bummer)
It takes a bit of practice, but is actually easy on the Rega. as the LP hangs over the edge of the platter slightly.
IF you cannot get the hang of doing the moving Lp snatch, then do not worry about turning the TT off and on.
I owne a Rega P5.
The moving Lp snatch is harder to accomplish on my Kuzma, where the platter is wider than the LP...

Thanks for the responses!

I've been able to do this with relative ease and I'm sure with practice it will come even easier. I just wanted to be sure I shouldn't be picking it up while the platter is spinning! I do have a Black Joe Lewis 8" EP that was a bit more difficult.

Elizabeth - I listened to the P5 on Friday as well.....when budget allows, that WILL BE my next step up!

I suggest those with VPI tables with center weight and outer ring to position these with the table not running.

I have my table placed so that I can run around it at 33 RPM so the record remaind stationary relative to me; this makes changing much easier. Seriously, this sounds totally unnecessary to me and this is the first time I have ever heard of the idea.