I hold a REIT (VNQ) but think it's dumb and I'd swap it if not for the taxable event. What I've realized since buying it is that you get a ton of exposure to real estate through most index funds. For example even McDonald's is primary a real estate company (SP500 #29). Tons of companies are heavily invested in real estate. Public Storage is in the SP500. Even tech companies often own a ton of office space. Google's real estate is worth over $10B.

If you want to be overweight on real estate -- really ask yourself why. Apply the same logic as you would to choosing a specific company, which is the same logic as trying to time the market. It boils down to believing something is undervalued now or will be overvalued later, and the truth is you don't know, you can't know, and if you guess you'll probably be wrong. So don't bother.

Admit the market is smarter than you. Smarter than any of us. The best approach is just very broad diversification, and the best way to diversify is through total market funds. Total market funds gives you ownership in the owners of real estate. Buying REITs makes you overweight on real estate which is a bet. Market bets are always against you.