I should know better than to attempt to have an advanced economics discussion with the likes of HN readers ... many of whom for reasons I will never understand always jump to the defense of evil landlords. Landlording is not a job and does not add value or goodness to the economy or to society. Most people involved in the "For Rent" business have gobs of money, no skills, no actual work ethic, and no ethics period (try a Google search "Jared Kushner slumlord" for reference of one key example).
The proliferation of renting "for profit" in the last 10-15 years is the number one factor contributing to the acceleration of the division of the top 1 percent from the bottom 40 percent (used to be the bottom 25 percent, then the bottom 30 percent; now it is the bottom 40 percent), because there are no market forces slowing it down. More progressive income taxes could have slowed down the top tier just enough to give the bottom 40 percent a little bit of a break. But the rate at which the top 1 percent's income is growing is now even too much for that to have any effect. They write tax code for their benefit, own lobbyists, get unfair tax credits, and basically wreak havoc on the working class by stealing their equity. The article's citations of median rents in LA is evidence enough.
Current system: When landlords have more profit to buy more units, they control more supply and are thus incentivized to further inflate rents, ad infinitum. Clearly price-side economics favors those setting prices. Rent controls do not really work, nor does any system that attempts to make renting "affordable" for working class people because it's basically just pouring more money into an already broken system. Lift people up and out of poverty by giving them incentives to escape the broken system rather than forcing them to stay beholden to it.
The reason the tax on rental income would work is it would make renting "for profit" prohibitively expensive for landlords. Sure, they could try to aggressively increase rents, but it would work against them because for every extra dollar of rent they tried to suck out of people, they'd only net 35 cents. Furthermore, a fresh injection of supply would hamper their efforts to buy up all the supply in consolidtions. Rather the small and independent landlords would have to focus on keeping their current renters happy (like by offering real customer service) and improving the quality of the rentals they manage. Imagine that!
The solution is to make collecting rents an unappealing and unprofitable avenue of investment. And it would work.