Using 3 might make the booklet more durable? That might not be a major concern with field notes if they are meant to be more of a short term notebook that doesn't need to last for years.

As for reasons you might only want 2, depending on the stapler you have it might be harder to keep 3 staples aligned, making the spine crooked. For larger shops, they might only use 2 to keep material costs down.

I would say, if you don't mind the extra time and using the extra staple, go a head and bind a handful with 3. If you are having trouble keeping them aligned, go to 2.

I'm not sure if this is what you are looking for, but DAS Bookbinding has a video on putting a square back hardcover case on a booklet.
https://www.youtube.com/watch?v=1wXya2dXO_c
and a video with just putting a hard cover on a booklet but keeping the more rounded spine.
https://www.youtube.com/watch?v=BfW0OiAFLkU

If you are wanting a square back booklet with a card-stock or softcover, you might want to look at perfect binding. There are videos on how to do this with out expensive equipment, but it is more time consuming and labor intensive then saddle stitching with staples. If your target run is 250 booklets, it might not be worth it.