Kirk saw himself as the best option to lead this particular crew into this particular situation. Wanting his ship back was in the back of his mind and did influence his initial attitude, but his instincts turned out to be correct.
Or then he just wanted his ship back, and for that was ready to stake the entire planet Earth. Two ways to view Kirk's massive hubris, not all that different from each other in the end.
What was Kirk's input in defusing the crisis? None that we can discern. Spock did all the crucial things: he understood how to communicate with the cloud and get it to suck the starship in instead of blowing her up; he understood how to communicate with the thing inside the cloud; and he understood what the weaknesses and desires of the thing were, and how to exploit them.
Perhaps Kirk should be thanked for bringing Spock aboard the hero starship so that the Vulcan could save the day? Well, not really - Spock seemed determined to meet with the cloud anyway, and had a spacecraft at his disposal already. Sure, it helped that the Enterprise
had shields capable of withstanding V'Ger's first bolt, buying time for Spock to discover the solution; but Spock might have approached the cloud differently in the first place, coming up with a solution before any bolts were fired.
Make no mistake - I don't fault the movie for making Kirk seem completely redundant, in addition to being rather repugnant. Rather, I appreciate that! It's an atypical treatment of a hero, and a welcome one for the sheer variety...