You can wear as many hats as you can manage but:
Mandatory:
Designer
Writer
Programmer
Artist
Non-mandatory but highly advised:
Tester(s)
Editor
Quality control
Proof reader(s)
(at least one of those, preferably at least one of Editor/proof reader and one of tester/QC)
Others:
PR, it always helps but frankly the main dev should doing this as the "face" of development so it's not a job that needs filling rather just something you should be doing.
To be honest though you need to tailor the team to the project, something text based like monster girl dreams doesn't need a full time artist but could use an additional writer whereas you may need multiple render monkeys for a big VN to be done at a reasonable pace, look at superpowered that game is huge and slow to develop because the dev doesn't have the level of staff to make the game in a reasonable time frame.
It's not a one size fits all sort of thing, plenty of devs i know do the whole lot themselves but speed suffers, in my opinion to be an effective boss you need to be able to do 75% of what the guy your directly responsible for needs to do otherwise stuff gets lost in translation, as a guy who is responsible for people in my IRL job and who is very much first ass in line for a kicking when something goes tits up much like a main dev is if something goes wrong, you need to be able to get your head around all of these jobs to at least a functional level IMO, yes even the programming and art.