FWIW, I agree with gastropod and the others. I wouldn't buy an investment property purely for the sake of diversification. If you think you need more real estate exposure in your portfolio, you can always buy more REITs like VNQ.
Mom 'n pop real estate investing can get you outsized gains in large part because it in effect opens up a bunch of highly remunerative side gigs. You can become a part-time market analyst, rental manager, maintenance guy, landscape architect, renovator, broker, etc. Any of those things you take on yourself, if you do them well, will earn you more money than bottom-line market returns. If you have no interest or time for that stuff, then there's probably no sense in it.