Leaving one type to do all the ruling in the world is inherently a bad idea.
You may like the idea but I've met too many INFPs that can become downright vindictive if challenged. If we had enough INFPs that agreed on everything to rule the world, it might be doable, but I doubt you'd be able to find enough of them.
And you'd have to have enough bedlams for all the TJs that would go mad under your regimes. You may want to huggle and snuggle us, but we wouldn't like it very much.
In as much as those who type as INFP are human, I would expect that a world run by INFPs would suffer the consequences of any single type ruling - the difference being the fallibilities would present in a specific way.