I feel a bit concerned about the ramifications of this. Specifically, Jiraiya just spent approximately a full month or so away from Leaf immersed in negotiations with the other Kage, and after factoring in the break the negotiations took over two months. If the Chuunin Exams happen every six months and Kage obligations go roughly like this each time then Jiraiya (and the other Kages, for good measure) are each spending a full sixth of their time off negotiating with other Kages and a full third of their time with negotiations ongoing.
To be perfectly honest, I'm worried that spending so much of your time away from the village you lead is potentially unsimulationist, as is keeping the Chuunin Exams running half as often as not. There are a few things I can think of that could mitigate the concerns I see here:
- Longer schedules. Annual exams halves the severity of all of those obligations and means the Chuunin Exams are offline much more than online, and wider timeframes would ease it even more.
- Have it so that regular exams don't take as much time for Kage negotiations and this one's important enough for Jiraiya to be in Mist all the time.
- Have it so that regular exams are much shorter in general. We know Mist was drawing this one out, but if a regular exam gets all its events knocked out in a week then the Kages really aren't stuck away from home too much.
There's a decent probability as I see it that you've already been using one of those and never said anything because nobody asked. It also looks like decent odds that you've structured your picture of Kage duties and activities around the Exams being a focal point for international relations in such a way that taking up a large chunk of their time is perfectly fine. I'm trying to cover my bases because I'd hate to find out down the road that this was a plothole all along.