Uh, the use of Termina Field is to link all of the areas together. Without Termina Field, all of the main areas would be right next to each other, and that would make all of the different areas pointless. If they were all just in the same general area, it would leave out any need of there being multiple kingdoms and just create one big area. Where would the dungeons be? In fact, I bet the Giants wouldn't be imprisoned like they are in Majora's Mask if there was just a single kingdom in Termina.
Aside from that little bit of information, there's the obvious; there's a Hyrule Field, so there needs to be a Termina Field. They're parallel dimensions, and they mirror each other, very much like the Light World and the Dark World. If one thing happens in one will happen in the other, just with a slightly different way. They wouldn't be parallel dimensions if not for their similarities in landscape, people, and a few other factors.
As for the bird, just wear the stone mask. It won't ever see you coming, or you can always just wear the Bunny Hood or ride Epona and zip right past him. If you need the money then an arrow, or a spin attack will earn you some quick rupees. And of course, if you do get your sword stolen, you can easily warp back to the first day and your sword will be there for you again. It may take up a bit of time, but you can't afford to be lazy in any Zelda game.
So aside from the fact that you need to have the kingdoms connected, and Hyrule and Termina are parallel, Termina Field really is a great place. It's a good source of money, and the music in the background is great. I think that Termina Field was a very great place.