While some won’t like the idea of bringing in James Kirk, him being involved in some proximity makes sense. For this entry and the next, the idea wouldn’t be to have Kirk on the Enterprise but used in more of an occasional guest start. Someone that the crew runs into while they’re out on their adventures.
Maybe he’s in the brig for disobeying a superior officer or getting chased down by a jealous ex, or a jealous ex’s boyfriend. Putting him on the Enterprise itself would seem to re-write some more history than needed. While the new series has done plenty of retconning, you don’t really want to keep doing that.
The fanbase has already had enough people turn away from Nu Trek, the last thing you need to do is find new reasons to turn people away. Keep Kirk as an accessory character, something to add to the plot of an episode, not to change the course of the series.
Bringing him in would also give Captian Christopher Pike a chance to influence Kirk, and lay the seeds of who he’ll eventually become. While Spock did serve/will serve under Pike on the Enterprise, that doesn’t mean that Pike wouldn’t have had a far-reaching impact on many Starfleet officers.