This is my idea(s) for a new captain. Please don't take this posting seriously.
Human Captain - male human of Irish/Mormon background,hence extremely conflicted due to this background. We could have a episode where he discovers the planet where his late dad lives thus validating his religious beliefs.
Or of German background who has a very dark past. He once broke the temporal prime directive & travelled back in time to the late 1930s and became the personel groomer for Hitler's pet dog, blondi. As a result he is also highly conflicted.
Ferengi Captain - makes folks pay for visits to the sickbay as he lives by the motto "if healthcare is free, the quality WILL suffer"!
Klingon Captain - openly gay, likes to bite male humans on the face for some reason, has the largest collection of early 21st century hello kitty memorabilia in the quadrant.
Bajoran Captain - orphaned during the Cardassian occupation of Bajor. He was raised by an African American couple on earth. He is into 1970s culture as his mother is a historian on the 20th century. He jive talks and calls Cardassians "honkies" behind their back.
Vulcan Captain - practises pederastry because it seems Vulcan culture accepts it. Lives by the motto "girls are for mating, boys are for fun"!
(Remember Vulcans are based on the ancient Greeks and ancient Greeks were into pederastry)
Or a Romulan Tal Shiar agent posing as a Vulcan but has a passion for the now centuries old human dance form known as "Krumping". Starfleet intelligence get suspicious when they realise Vulcans don't dance.