The general idea was that Spider-Man would be rebooted after three films
No, that was not the general idea. At the time of SM3's release, Raimi was discussing a possible Spider-Man 4
, while Maguire said he would return if Raimi was the director. The film was not going to be a reboot. When the bottom fell out of that chapter, it was decided that a reboot was in order, thus it proves the point: if a series as successful as the Raimi Spider-Man
films was rebooted in favor of another vision, Star Trek can face the same fate.