The second two points are, in fact, correct if the factories are Privately-Owned. It's the first point that is what this thread is arguing about, whether capitalists are really using their money to build factories or "the government" being viewed as the player is dictating to them what to do with it and if the latter is the case how that's bad and is making every economic system play as an "absolute command planned economy."
Well, if player plays as capitalists, then player builds and owns factories, player automatically get profit from them, spends it automatically on some needs and then player puts remaining money in his investment pool. Also player does the same with state budget. Effectively player control and can plan and command the whole economy inside his state. From POV of player this is exactly command economy: he, as player, is building, planning everything.
I agree, there would be nuances of "you can build only these buildings with this pocket and you can't unconditionally subsidise them" that could make your decisions and goals different and significantly (Here, on this forum, are a lot of threads on this very topic). But how you implement these decisions in life is the same: you choose place, building, your pocket and then just build it. And from variety point of view this is a huge missed opportunity compared to possible further development of vic2 ideas, which could not only make difference in which decisions you want to take, but also how exactly you will implement these decisions. And this difference in "how do you implement your decisions in life" could influence decision making itself, it will break this "commanding economy" feel at the very least.
If you want some example, how this flattening, samefying of gameplay is happening, you don't need to go far away: take something like eu4. All states have different parameters like national ideas or governments, limitations, mission trees, geographic position, etc, it definitely influences your decisions and goals: yes, England or Muscovy or Venice all play differently. Yet, on the level of what you are actually doing, how exactly you are implementing decisions in life, it's all almost the same, extremely streamlined (not counting some magic buttons). The only place that has a bit a distinct thing about what you are doing is HRE, yet, due to streamlined player agency, differences are not that big. The opposite example would be something like ck2: playing as a republic one is building trade posts, potentially conquers local towns and fights with money and intrigue, which family would rule next term and will be able to siphon republic income for a bit longer. While norse raider can just sit at his cozy Sweden and amass riches by raiding Rome or Paris. The same holds for vic2: LF, due to inability to build and subsidise buildings, has differences on a level of what you are actually doing while developing your industry, compared to Planned Economy. Sadly, LF was not given enough toys to play and levers to pull, to make it possible to influence capitalists, to make playing as it more engaging. But these toys and levers could have been given. The ability to pass laws that give you different toys could be given. Yet again, it feels as missed opportunity to just give player a direct control over capitalists investments, not counting loss of additional benefits of having internal but independent agents.
As much as i want it, I don't think that vic3 should really have capiAI, honestly, because the game is already designed for direct building of stuff by player, it would be like making AI to build stuff in Anno and giving you some hastily built tools to influence it, which would not satisfy capi lovers and will only irritate capi haters. I think, Wiz should carry his vision right until the end so people, who like his vision, would enjoy the game, it definitely will be a good game for them.