Star Trek is a different beast altogether. Kirk, Spock, McCoy are the iconic characters of Star Trek. As fans we may like all the others too but they all stand in the shadows of those original characters.
I think if you can't get away from having to have Kirk, Spock, McCoy, then Trek should not continue.
There's a HUGE universe in Trek, but to keep going back to the well and endlessly recast/remake/reimagine/recycle those three like they are comic book icons is pathetically uncreative.
Obviously it takes a lot of work to come up with new characters that can match the popularity of the originals, but darn it, why can't writers exert a little effort??? Someone had to conceive of Kirk, Spock, and McCoy in the first place. It didn't just spawn out of the ether. You just get cracking and come up with something new.