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Investors are people who invest in different businesses and I doubt Bitcoiners are also investors.
Although we won't know, because there is no real data as you said before, I agree with the intuition that the profile of the Bitcoiner is more like the one stop shopper you said, and instead of investing in different businesses like the traditional investors do (diversify, not all your eggs in the same basket...), they will be investing in different altcoins instead, and in the case of maximalists, not even that.
And yes, I agree with a profile more inclined to gambling than investing, although there are also stone hand HODLers who will stack even the last sat.
There are no statistics for this but I must tell you that Bitcoiners are regular people too, so what is happening in the lives of regular people is what is happening with Bitcoiners too. Many might tell you that they invest in only Bitcoin, but it's a lie, most of such people have altcoins as they are trying to diversify their portfolio and also make more return on their investments.
But for another asset in the traditional market, many may not get involved in that truly, but it's not for any other reason other than they are not just inclined to that. If not for Bitcoin and cryptocurrency, there are a lot of people who wouldn't have known about investment not to talk of trading. However, this is not because they wouldn't want to try to gain their own slice of the cake in such investments but they just do not know other means by which they can invest and make money. Also, for the fact that some already know cryptocurrency and are gaining from it, they might not want to bother themselves with other means of investment.
This is the way I unbiasedly see it.