I went round and round with this question. I ended up doing the ceiling the same color as the walls. It was high enough to accomodate lots of color. I think it's 16' at it's highest point. Mine are more sloped on the side and I have beams but here's what mine looks like. The painters still need to touch up the paint.

depends on the state of the ceiling, really - because that's the primary reason behind a flat paint - you can use it on a ceiling because it's not subject to hand prints, and it's good because it hides small flaws that show up on other sheens. but in a bathroom that involves a shower (humidity, etc) I prefer an eggshell that I can wipe down seasonally. by the way - that 'should' is one of those 'decorator's rules'... and decorating is kinda fake by its very nature, and a whole different thing than people living in a space, and making it beautiful as well as functional.

do you want glossy? glossy will show every imperfection, so make sure your install is nice and clean. If you're going to prime, try and do a very fine sand after the primer to hit any rough spots. clean well before painting. are you doing white paint? I think anything from eggshell to gloss would be fine. just depends on your preference. Use BM Advance. they have the best glossy paint. SW Pro Classic is 2nd. this one looks like a semi

Sorry, it was late last night when I sent you the two links. I understand the hesitancy. Simply white is the right undertone, but may feel a bit too yellow, a bit too colorful when you are looking at samples vs looking at an entire wall. I also get that painting trim and ceilings is not inexpensive and something you don't want to make a mistake. @Beth H. : is one of the pros who posts often on Houzz and I believe I remember some posts from her where she stated that she had used White Dove and re-painted with Simply White. I think she used it on her Trim, Walls and Ceilings, but maybe she will see this post and chime in. There is not a color out there that works 100% of the time in every home. There is a reason that I didn't pick a ready formulated white and used the color match to icing. Although it is very slight, the difference between Simply White and Icing is that Simply White has a bit of gray added to the yellow, where Icing has orange. Both are very light whites, both give you a touch of warmth to soften the feeling, but I notice the slightest green tinge in Simply White that I don't see when I use Icing. Simply White would be my first choice if I had to choose a white from one of the stock formula whites from BM or SW. I am not sure that anyone would see a difference if I would have chosen Simply White instead of Icing, but my OCD took over the decision making process. Here are two photos of my foyer using BM Frosted Toffee (walls and ceiling) and Icing (door and trim).