It would have been just as easy to have cast the same people but as totally new characters with a new ship, etc. Reworking TOS was always going to get the backs up of the series' fans.
Well, not to rehash this issue for the umpteenth time, since, as you said, done is done, but I was just objecting to the (oft-stated) assumption that rebooting TOS was bound to "get the backs up" of us old-school fans.
Here's the thing: enjoying a remake or reboot does not mean rejecting or replacing the original version. I grew up on TOS, but I don't take the very existence of a new version as a personal affront, anymore than a new version of TARZAN or SINBAD offends those of us who grew up on Johnny Weismuller or Ray Harryhausen.
So we shouldn't jump to the conclusion that rebooting TOS was inevitably going to tick off the long-time fans. Sure, some fans took issue with the idea, but most of us didn't. (Any more than Bond fans rejected SKYFALL because it didn't star Sean Connery and wasn't based on an Ian Fleming novel.)
It's not like the new movie only appealed to non-fans . . . unlike what some people like to think.