While some parts slowly degrade with running hours, the bigger issue is probably the energy use -- cost of power, etc. There's also some security risk. An unauthorized person could hit your PTT button. Also your rig is somewhat more at risk from power/lightning surges when powered on. Summing up, don't lose too much sleep over this. :-)
Thought for Flex: offer an optional auto shutdown after N minutes of user inactivity.
The only moving parts are the fans and the relays. The only consideration would be the fans. They will wear out, but they have a high MTBF so I would not concern yourself with that too much, and they are easy and not expensive to replace if a sealed bearing fails.
One other concern might be dust. If the radio is operated in a dusty environment, then you may need to clean it out occasionally. If using compressed air to clean any type of cooling fan, make sure the stream of air does not spin the fan when cleaning. That can damage the fan.
My Flex 6300 drew using a Astron RS-20M 55 watts in receive
510 watts transmit 6 meters
400 Watts transmit on 10 meters
375 watts transmit on 40 meters
379 watts transmit on 160 meters.
If I were to leave it on here where electric rates are high 25 cent/kw it would add about $10 to my bill.
I have consideration for the planet I live on so I shut it off.