I don't see any real issue of new investors "buying both chains" during a fork, because it should be pretty much over in minutes in the on-exchange arbitrage situation I described above. It would only affect those people who happened to make the decision to start investing in Bitcoin during those few minutes and couldn't wait.

Now in the unlikely future event of a real schism with two persistent forks, it doesn't affect current investors. They can sit tight and whatever happens their money is safe. For new investors of course they have to make a choice (or hedge between them), but that is natural given there was a real schism in the economic majority, which suggests there were good reasons for it. I don't think hardly anyone is going to invest in a smallblock fork versus a reasonably larger block fork, for example. If we assume a major schism where investors support both, which seems very unlikely, then there was probably a good reason for it.