Let's see, Romulus is gone, Vulcans are emotional and fall in love easy, Uhura and Spock are lovers, cadets get promoted to captains and commanders.
They still drove cars in the 23rd century, humans are rude to each other...
Nothing's changed, why not?
Though I agree, they do have to find a new way to present Trek in order for the series to survive on TV.
Romulus is still there. It's Vulcan that's gone. Vulcans have always been emotional. (Spock especially), there was a spark between Spock and Uhura back in TOS, I'll give you the last one. Though McCoy is the only person who seems to go from cadet to (Lt) Commander. But being a doctor its not unusual.
Why wouldn't people drive cars in the 23rd Century and why would they stop being rude? Rude wasn't unknown in TOS. One might find examples in almost every episode.