The thing is, there's a year-long time jump between the climax and final scene of STID as it is, so presumably the Klingon tensions were resolved in the interim. Besides, STID made some dubious story decisions, and for that matter, so did the first film. I liked a lot about them, but they had their shortcomings, and I'm glad the STB team made a clean break.
Besides, the real story arc of these films is not about galactic politics or war, it's about the formative journeys of the TOS crew. It's about the young Kirk, Spock, McCoy, and the rest growing into the people we know from the 5-year mission. And the trilogy gave us that journey. Kirk was a cocky young cadet in the first film, he learned more humility and responsibility in the second, and in the third, he'd finally matured into the Kirk we know. The origin-story arc reached its conclusion in the third film, which I assume was always the plan.
Not to mention that STB was the first film in Kelvin, and one of the few Trek films overall, that actually involved the frontier and strange new worlds. The point of Yorktown was that it was right on the cusp of the frontier, the interface between the Federation and the new civilizations beyond it, serving as a diplomatic headquarters for new contacts and a command base for exploration. Making it just some border outpost that the Klingons attacked as a political retaliation would've taken away that frontier aspect that too few Trek films have been willing to use.