If you do it that generically you can just as easily line up the casts of Next Gen, DS9, Voyager, Babylon 5, or Stargate. Having an engineer, a doctor, and a vulcan doesn't mean its the same.
Going from your list, I'm not sure if you're saying they're the same because of their race, accent, or because of their role on the ship. Either way, it's not really lining up.
Having similar roles doesn't make them similar characters in design or execution. T'Pol for insance wasn't anything like the emotion holding Spock at all, she was angry, impertinant and barely even a Vulcan, to the poin many theorized she was secretly a Romulan. Tuvok on Voyager was much closer to Spock. And drunken loony redneck engineer Trip wasn't anything like stern elder doctor McCoy. And that you're splitting Sulu two ways based on… race? is pretty telling that its not a close match at all.
Next Gen had
Riker for Kirk as actioney leader
Data for Spock as logical science guy
Geordi for Scotty as engineer that could do anything
Wesley for Chekov as the young kid enisgn
Crusher/Palaski for Bones as the doctor
Troi for Uhura as the one wearing outfits that are not appropriate uniforms.
Or we can go with "Black Scotty" and "White Chekov" and "Woman Bones" (especially with Palaski) if that fits your standard better. And hey, Voyager had a female Worf and a black Spock and a female captain! And all the shows had a doctor!
As for reusing plots? Next Gen stole from TOS constantly (especially in the first two seasons) and then later DS9 and Voyager stole from them. You get overlap in long running franchises.