But your scenario is rarely if ever the case. Especially when referring to new housing, because landlords and construction companies are typically different entities, so when the new construction is complete it goes for sale into the market and anybody has the opportunity to buy it.
Meanwhile buying up an unbounded amount of newly constructed housing only to leave it idle would be extremely unprofitable, because they would have to be paying the construction companies the existing market rate (i.e. the monopoly price) to keep someone else from getting it, but then couldn't rent it out and recover any of the money because that would increase supply and lower prices (or, to put it another way, no further renters can afford the monopoly price so their choice is a lower price or an empty unit).
Meanwhile buying up an unbounded amount of newly constructed housing only to leave it idle would be extremely unprofitable, because they would have to be paying the construction companies the existing market rate (i.e. the monopoly price) to keep someone else from getting it, but then couldn't rent it out and recover any of the money because that would increase supply and lower prices (or, to put it another way, no further renters can afford the monopoly price so their choice is a lower price or an empty unit).