I am not convinced that gifting yourself is a good idea. It simply goes against what the holiday is supposed to be about... especially on a game. Besides that, you can get a large amount of gifts from the secret santa if you do it every day, so the amount shouldn’t be an issue.
I think that being able to pick what you’ll receive from the secret Santa would be nice... though that wouldn’t make it very secret, I suppose. I think being able to have an “auto message” for secret santa gifts would be nice, because I agree that sending in bulk is a pain when you don’t know who is getting the gift and don’t know what to say to them besides “Merry Christmas!”.
Mystery gift sounds fun, but since opening presents already is really intense on the server resources I’m not sure they could pull it off... it’s still incredibly laggy and that’s even with the times that people can open gifts being staggered.