This still doesn't make any sense! Lower rent is worth more than no rent and the property appreciates either way. Keeping a unit off the market to keep the rents up is kind of a silly plan if you never end up actually renting any of the units.
Ergo, lower rent is not always worth more than no rent, even all else excluded.
Example: you rent your property to a tenant for $100 / month, who does $5,000 worth of damage to the property, and declares bankruptcy when you sue them for recovery, in addition to the time you spent installing them + evicting them + dealing with recovery.
Keeping properties off the market for years at a time in order to mitigate the risk of actually having tenants is not a very good plan.
If lowering the rent by 10k a year lowers the value of the building by 100k, the building owner may have to add 25k that they don't have to keep the building from falling into default. If you have a completely empty building and you accept a lower rent in one of ten units, you could need to put down 250k it of you have many building under one loan they may want millions because of how it changes the loan valuations.
People don’t keep units empty for tax breaks. That’s absurd.