When your tenant does not have enough capital to pay the deposit and first month’s rent to move into a new place, they will not have the capital when their car breaks down, or they have any other mishap with their finances. They will be short rent, and you will be out rent. Good tenants have a financial reserve or plan for emergency expenses. If they are good tenants, they will be getting their deposit back from the old place, and will then be able to use that to replace their financial cushion they used for your deposit. A good tenant shops around, but knows a damage deposit is required. They also know they will get it back, because they will leave your unit in good condition.
When your rent is at the top end, you are going to be renting to a subpar renter, almost by definition. Good tenants can go anywhere. Subpar renters get rejected by all of the big-box places, and have limited options. Subpar renters need to pay more rent, but do not have enough money for a deposit. A subpar renter believes they can pay the rent, and know if worse comes to worse, they can pay you later or move out. They do not have much to lose, and they do not have much of a deposit invested. If you really want these subpar renters, lower your rent so they can afford it, but you are far better off waiting for a qualified tenant.
Have you ever lowered the deposit for an incoming renter? Did it ever work out? If you are a renter, have you ever requested a lower deposit?