Honestly, the "Monty Haul" and "Historical Simulator" I don't really agree with, they don't really fit in as play styles in DnD. Maybe in other games, but with the "Monty Haul" regardless of what work the characters are doing, it's still weighed as a risk vs reward, even if the risk is small and the reward is great. Players are still going to weigh the two and decide if they are going to do it or not. "Historical Simulator"...well...I mean, you can't really do that unless you rule out all magic use, which at that point why even bother playing DnD. Now if this is viable in a different system more power to you, but I have only ever played DnD, so I can't say one way or another.
The rest you can do if you plan it out properly, so I agree with those. Though, I have to admit, that I believe most people play with a mix of these depending on the campaign they want to run and the players they are with. I don't think anyone truly plays with purely one play style unless the group has asked for it, all the players fall into one of the categories you've mentioned, and/or the DM falls into one of them. What I will say in my opinion is that these categories aren't targeted at just one type of person. I myself love just hacking and slashing and being in the fray, but I am also really good at puzzles and riddles. I wouldn't call myself just a thinking as you mentioned in the Problem-Solving section, and I wouldn't call myself a younger player with that mindset also like you mentioned in the Hack and slash section.
Ultimately I do agree with the description of these categories, but I don't agree with who you are classifying into them, if that makes sense.