You want good hard wood. Having the fret board be separate piece makes the building make sense. I made an electric mandolin neck out of 1 piece of Maple. I did that as a nod to old Fenders that were made that way. I have seen many Mountain Banjos with no fret board, often no frets as well. I like neck wood to be quarter sawn with as little run-out as possible. A solid maple neck will be heavier than a Mahogany neck with a hardwood fret board.

The 1 piece mandolin neck in the picture was made from a plain old board. It is not quarter sawn and has lots of run-out. It is for a novelty instrument.

Separate fretboards offer a number of advantages. For one, it's easier to make the neck, since the trussrod channel can be cut from the top and gets covered by the fretboard. The different type of wood also helps stabilize the neck -- keeps it from warping, twisting, bowing and bending. Also, different wood types are easier or harder to work with - you wouldn't want to carve a neck made entirely of ebony. If you're making your own, if you mess up -- say in cutting the fret slots or making your own inlays -- you can start again without throwing out the whole neck. If you're into aesthetics, you can use the fretboard for the contrast in colors, or use exotic woods (I made a neck with a tigerwood fretboard, really beautiful). Also, it's easy to buy pre-slotted fretboards.

I believe most one-piece necks are maple?

Here is an official banjo neck blank. It was "gotten out" of the log as a billet rather than a board.

Definitely not essential. Look at the Goodtime line of banjos, or Telecaster electric guitars.

But as said above, if you want a truss rod, you're going to need to cut a channel and then cover it over. People usually cover it with a fingerboard, but you could also do a skunk stripe down the back of the neck.

Here is how I did a non adjustable carbon fiber neck reinforcement in the back side of the "no fretboard" neck. This is similar to how an adjustable truss rod is put into the one piece neck of a Strat. or a Tele. (as mentioned above).

My first banjo was a Japanese import with a decent tone ring and rim. But the neck had some relatively soft wood fretboard which wore really poorly. I had gouged out some big grooves after a few years of playing. Since then my high end banjos have all had ebony fretboards, which show little wear after many years. Maple and mahogany are roughly half the hardest scale as ebony. Something to think about if you go with no fretboard.
Rick