Assume for a moment I could demonstrate that all three of those reasons are false.
I am having great difficulty imagining that. I've lived some of my life in Winnipeg, where temperatures and wind-chills can hover for long times at the worst I experience here, and often enough, the weather report includes a detail along the lines of "exposed skin can freeze in X minutes". But, for the sake of argument, I'll try to imagine that you have some clever alternatives that provide equivalent protection without significant downsides (such as trying to carry several bags of groceries while one hand is occupied with a parasol, or getting a deep tan that doesn't increase the risk of skin cancer).
Would you stop wearing a hat?
That is, would you bet wearing a hat on the veracity of those reasons?
I've signed up for cryo; I think that demonstrates my bona fides in my willingness to do socially strange things to improve my quality of life, given a reasonable confidence-versus-pros-and-cons analysis. If you can explain how not wearing a hat will improve my life in such a way that I can compare your claims against the evidence, then I expect I will reduce my hat-wearing frequency appropriately. If you don't, I probably won't.
I don't see any reason to make an actual bet, unless there are stakes on both sides of the proposition instead of just one.
(Now that a local heat wave has broken and it's feasible to take a walk for pleasure, I expect to buy a new hat by the end of the weekend. I'm currently leaning towards a simple, white baseball cap to insert the Crasche panels into. Which, as I'm typing this, makes me realize that I might be about to become a literal white-hat hacker...)
I didn't say that the reasons were bad. I said the reasons were false. That is, they're not your real reasons for desiring a new hat.
Because you're not buying a hat to protect against both heat exhaustion -and- extreme cold. Apart from the contradiction there, you already -have- hats for these purposes, or these purposes would have come up in your original request. You're looking for a hat for which -neither of these conditions apply-, or else they would have entered into your specification. And if neither of these conditions apply and your desire for...
For years, I've taken being a classic nerd, geek, and hacker as a point of pride - eg, consciously trying to judge people by the code they produce, or whatever else they write, as opposed to judging them on their appearance, to the point that I prefer /not/ to know what my favourite authors look like. I've tried to make what strengths I can out of the resulting weaknesses, such as reducing decision fatigue by keeping a single hair-style for many years, wearing whichever t-shirt is on top of the clean shirt pile, and so on.
I'm no longer satisfied with this. I want to become stronger.
Last month, I bought a dozen button-up, collared shirts... and have noticed slight, but consistent changes in my workflow when I wear them. I want to leverage whatever other clothing-based self-improvements are within my budget.
For some years, I've worn a floppy boonie hat to shade my delicate eyes from the burning rays of the sun. (I've even been seen wearing it with a photographer's vest instead of a daypack while tromping around my hometown.) I'm thinking of trying out the 'Crasche' safety inserts mentioned in the recent Open Thread while hiking far from medical help, which would require a baseball-like cap with a sweatband. Given my proclivity for taking something that works and sticking with it for years, I might be wearing that cap for a very long time.
Thus, a multi-layered question: Which hat should I buy? Which factors should I take into account... and which shouldn't I? Are there any subreddits, forums, or other online discussion groups whose members would be willing to take this question seriously and with only a minimum of mockery?