xviper

No, you're not stupid and 2nd gear is no problem to leave it in but not for the reasons you think. When your car is idling like just before you turn it off and that's when you might normally put the thing into 2nd, the synchros don't get much of a work out at all. While parked with the engine off, the synchros don't come into play at all so here, they can't get damaged. Synchros get used and possibly damaged when one spinning gear meets another gear spinning at vastly different speeds.
I use 1st mostly because that's the last gear it's in just before I shut the car off (unless I just backed in).