The same thing that keeps everyone from investing in any "on average" profitable space - risk and opportunity cost.
Renting a house isn't always profitable, for a wide variety of reasons. Maybe you can't find tenants, maybe the house has unexpected maintenance costs, maybe you get into a costly legal battle with your tenants, or maybe the house is destroyed by a meteorite. There's simply no guarantee that the income you get from rent will cover the management fees, property maintenance, tax, and mortgage payments. How much margin do you have in terms of vacancy time and maintenance costs until your great investment turns into a money sink? Collecting rent that exceeds your usual costs is a great plan, right up until you find yourself unable to collect rent, or with additional unexpected costs, or both.
Even if you turn a profit, how much profit? Any dollar invested in a house is a dollar not invested elsewhere. If you spend $100k on a house to earn $1k profit per year, you have a poor return rate of 1%, which could easily be outperformed by even very low-risk investments. Even considering the value of the house itself, there's no guarantee that the property value will go up. Collecting rent that exceeds your costs may look like profit until you go to sell the house and find out it has decreased in value - although you've made some money in the short term, it's possible to lose even more in the long term if the asset depreciates. Earning $1k/year in rent profits is not helpful if the property falls in value by $1.5k/year.
On average, real estate investment and property rental may be a good investment, but it's certainly possible that you make less than you would have with other investments, or even outright lose money. A house is also typically a large investment, which could make up a large portion of an individual's asset portfolio, resulting in a loss of diversification and increased risk. Buying three beachfront houses in the same area, for example, could result in financial ruin if sea levels rise or the local beach shuts down. Investing that money in a well-diversified index fund, in contrast, would be much more robust to the effects of any individual, local event.