I'm more concerned about the scope damaging itself, eg, a limited lifetime i don't want to waste ^^;
Nope. In theory better to leave it powered up actually, less stress on some parts. But don't go doing that just for the sake of it!
The V-212 is a lovely little scope, always had a very nice sharp trace, enjoy!
Yes & no-----waveform monitors were left on continuously,& their CRTs lasted twenty years or so.
If your 'scope has a linear supply all is OK,but there may be a hidden problem if it uses an early type SMPS.
Some of these use a high value resistor from Mains Active to give the oscillator a starter "kick".
Once it is running,all is well,but if the resistor went very high in value after the last start,the SMPS won't restart after ,say,a Mains failure.
It was "received wisdom" at the TV Studio I worked at,to leave everything "on"at all times------a reasonable idea in the tube days,where gear took hours to stabilise,but not necessary with Solid State.
One one occasion,a power failure left us with four Picture Monitors out of seven in Master Control as non-starters.
Not great,when you are the bunny who has to find & install replacements ASAP!
For this reason,I would suggest turning your 'scope off from time to time,so that if it doesn't restart,you are in a controlled situation when it fails & not have the failure happen when you most need it.