Why not - if you have the space. I know it is something that likely we won't do, because we don't have the space - and have a live tree. If I still had my blue tinsel table top tree, I would keep it up year round at the end of our bar.
A friend of mine used to have a "man cave" tree and had a mini tree that was decorated with various bottle openers and empty beer cans
I would love to make glittered red heart ornaments for a valentines tree! I also have a ton of plastic easter eggs somewhere just begging to be decorated.
I would love love love to do a Chinese New Years tree and decorate it with each year's animal - this is the year of the sheep/ram, coming up.
Plus - it would be a great fun way to celebrate the obscure special days - like Pi day, talk like a pirate day, etc! Or personal loves - like a Monty Python tree, or Muppets tree - except then DH would probably want it to become at some point a 3 stooges tree - blech....