Do you live in a walk up? The strategy works for a individual landlord or small entity because they are dealing with this kind of stuff themselves, but it's less successful for high-rise buildings with property management companies. Turnover is expected and they have funds and workers available to do this kind of stuff so it's less of a financial hit to them. They honestly don't even care and they know how much of a hassle moving will be for the tenant. Threatening to move doesn't phase them. They have more resources than you. With an individual landlord, it's a different story.

OP can try this, but it's not likely to work, or if it does it will get reduced by a laughable amount.