Did Star Trek need a reboot? This is the same question I posed many months ago. The answer? Truthfully, no. I also don't believe that anyone can justly argue against the answer of no.
You are by no means speaking for everyone . . . as the five zillion threads arguing this point suggest. Lots of us think a reboot was the right way to go, as we've "justly" argued until we're blue in the face. (Insert Andorian joke here.)
Do we know that sticking to the same continuity would work just as well? Not necessarily. Are there definite advantages to starting over again? So it would seem.
Besides, you seem to be working on the assumption that reboots are a bad thing to be avoided at all costs. That's also not necessarily the case. Reboots worked for BSG, for Batman, for Planet of the Apes, for The Addams Family, for Sherlock Holmes (three times recently!) . . . .
Granted, not all reboots works (Dark Shadows and The Night Stalker come to mind), but there's nothing wrong with the theory in practice. The Night Stalker reboot failed because it was done badly, not because it was trampling on the sacred memory of Dan Curtis or Darren McGavin or whatever. Or because it "violated" the continuity of the earlier version.
Preserving the "canon" of previous decades is not the be-all and end-all of storytelling. It makes for fun trivia contests, but not necessarily better movies . . . .
Trek was arguably overdue for a reboot . . . and where's the harm in that?