It's not a matter of "should". It's just not really possible to keep a paella pan seasoned the way one imagines seasoning on a carbon steel or cast iron pan.
Two properties of cooking kills seasoning:
- Long braising.
- Acidic liquid.
Paella is long braising in acidic liquid. :( Additionally the logistical inconvenience of getting out the large paella pan to cook other greasy things means it doesn't build up seasoning that could be sacrificed during paella cooking.
All the paella (i.e. the pan) manufacturer's videos on youtube don't show a seasoning process, they just clean the pan, dry the pan, and apply a little oil after use.
EDIT: I guess you could season the pan after every cooking session. That sounds quite inconvenient to me.