The higher you go in difficulty level, however, the more HC becomes a jack-of-all-trades-but-king-of-none
I've won with various leaders and settings, including deity. In single-player games the incas are as good as caesar on higher levels for several reasons. At monarch and above, you will see only archers and rarely any warriors from the AI. The quechua rush will give you a huge and early advantage in expansion well before any axes appear. The Incas are by far the easiest civ to win with on higher levels, and actually are not quite as good on lower settings. They especially thrive in crowded maps. Caesar will have to spend his initial turns doing his own expansion while the incas can start stealing workers and cities, and he will be unable to use his unique unit without iron (though that's not usually a problem). Even with the latest patch, caesar's traits are not as good for warmongering. Financial/Aggressive is an excellent combination, definitely better than Exp/Org for almost any situation. Caesar's main advantage is that praetorians will not become obsolete nearly as fast as quechuas. And you mentioned Tokugawa as being better than the incas for a domination/conquest win? Not even close. The samurai are a mediocre UU, while both quechuas and praetorians are among the most useful because of their early impact. Tokugawas traits are better than caesar's, but not the incas. Financial is generally better than organized IMO, though the gap was narrowed in the latest patch. The incas are definitely in the top three for domination/conquest wins, if not number 1, and the jack of all the other types of wins.
Not sure what you could say about state property. If you have a huge empire you should use it, if you have a compact empire then free market is probably better. That's all there is to it, and you can determine which would be better by counting your distance costs, civic upkeep difference, value of trade routes, number/distribution of watermills, and number/distribution of workshops. So if your point is, "Consider your situation and goals rather than dogmatically do what has worked in other situations," then I'd agree with you on everything except the incas.