If the mortgage is covered by extortionate rents on your other properties then historically the empty unit is appreciating in value.
Renters are in a position where they have no shelter if they don't acquiesce. Landlords have a multitude of options that make it easier for them to horde empty homes.
That appreciation is happening whether the unit is rented or empty.
The scenario the landlord sees for a given unit is (assuming zero mortgage costs just to make the math simpler [1]):
Empty unit: $0 in rent + $Y in value appreciation
Rented unit: $X in rent (X>0) + $Y in value appreciation (where Y is fixed between the two scenarios because both cover the same rental unit).
For the landlord, $X + $Y is greater than $0 + $Y.
The landlord's greatest total income is when all units are rented, as then all units are returning $X+$Y.
[1] including mortgage and tax costs adds two subtractions to the formulas above, which will result in a real net loss for an empty unit, as the mortgage and taxes must be paid, irrespective of the rented status of the unit.
Imagine the Landlord owns 10 properties and sets the rent to $2k/mo on all of them with 1 property remaining empty. Maybe that last property could be rented out at $1.7k/mo but from the landlords perspective that puts downward pressure on the rents of his other properties.
If one of the landlord's existing tenants moves into the cheaper property it's even worse. He loses $300/mo and now has to consider reducing the rent on an additional property. Should he find a new tenant at $1700/mo, he still feels like he's losing because he believes the rent should be higher.
From the landlord's perspective, it's better to squeeze if he has sufficient cash flow. Especially given the belief that lowering the rent will negatively impact the value of the property.
While you're correct that mortgage and tax are fixed costs that need to be met, you haven't considered that landlords have multiple options to offset those costs. When interest is low they'll use equity release and interest only mortgages.
I used small numbers for the sake of example, scaled up to a city it'd represent 10% of the city's housing stock sitting empty.