Does an Arduino get worn out by too much command execution?
No, the code doesn't "wear out" the MCU. In general no matter what you are doing roughly the same level of activity is being performed. Even delay() does lots of work while it's "idling".

There are commands to make the CPU do less - place it in an IDLE or SLEEP mode - but these are used to save power rather than to reduce "wear" on the MCU.

Of course there are specific things that do have a limited lifetime and you can only use them a limited amount of times - things like writing to EEPROM and writing to the Flash memory - so you don't want to be doing those all the time. Other than that, no, no matter what you are doing it doesn't wear the MCU out.