Wasn't Spiderman rebooted twice in one decade, or something like that?
I still don't think they'll reboot TOS because they've invested so much time in universe-building around it with all these new shows. However, there is a simple fix. Everyone says Kirk can't be on SNW because of his line in The Menagerie that he met Pike seemingly only once (when he made Fleet Captain). Simply put: Kirk lied to cover up the fact that he and Pike went on secret covert missions for Starfleet and the Federation aboard the Enterprise. These missions were classified, erased from the records, and everyone was told never to speak about them.
There you have it: Kirk in Strange New Worlds without violating canon.