It’s not a coincidence, it’s Pike. Pike’s seen the future and knows the Romulans are coming, and he also knows that Kirk being in command of Enterprise at that point has the best chance of succeeding at staving off the new war the Romulans will want to provoke in TOS: “Balance of Terror”.
He can’t tell Kirk that, of course, and he can’t do anything active to make it seem he’s planning for Kirk to take over. But what he can do is that if an opportunity comes to let Kirk aboard and become familiar with the Enterprise, her crew, and bond with them, he’ll take it. A joint mission with the Farragut and Kirk wants to visit? Sure. XO training with Una? Why not? Work closely with senior staff? By all means.
Eventually Kirk will be Pike’s explicit choice to succeed him, and at that point Kirk will have both the experience he needs and a familiarity and relationship with the crew and ship that will make him a plausible one.