There's actually already one, and it's called crypto20 I believe. It's pretty much just like a stock market index, it's a crypto index that invests in the top 20 coins in terms of market capitalization.
I don't think that this will ever become a popular idea, but it's happening out there already.
The reason is that you have absolutely no control of what you're investing in. If you are investing in coins traditionally by buying it and holding in an address that you have access to, there is 0 risk apart from the obviously volatile exchange rates. But trusting an investment fund to do something that you can do yourself already? Doesn't sound that good of an idea. They could easily deny access to your investment in the fund, if they really wanted to.
Plus, the lack of customization is a huge downside. There is no way that someone can pick and choose the coins they want investing in, but instead they're stuck with a limited range of coins in the fund that can't be filtered.
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i think it is mostly focused on older people , that don't have the knowledge to buy and sell on regular exchanges but still want to be invested in this space. this probably will be solved when the user interfaces mature and crypto becomes easier to use. because with all the stories around about hacking and losing funds i think a lot of people would rely on such a thing.