I don't think there's necessarily anything wrong with turnkey investments. It certainly has a much better potential than investing locally in your HCOL area where deals are few and far in between. Using geographic arbitrage without having to actually do anything can definitely good be a way to go.
Lots of things to look out for though. You still need to do a great deal of due diligence: research neighborhood, look for deferred maintenance, double check the numbers, vet the property management, etc. Since you should be going to those lengths anyway, it makes more sense just to do it yourself. It's a little extra work, but that's the point in real estate: leveraging your own time in order to receive higher returns.
I think most people are better off in index funds than buying turnkey, since the only reason to buy turnkey is if you didn't want any control in the property at all.