It's hit or miss for me... esp in Detroit market.
Some tenants will jump at it, but it's usually the tenants my PMs have a good rapport with. The others know, or can ask people who know, how to work the system and will attempt to drag out the process as long as possible.
We try to understand the good tenant's situation and say something like "the owner will give you $250 for a moving truck or a storage unit, but only if you have everything moved out by XYZ date, the house is clean/undamaged and we process your checkout forms w/out any problems."
If they verbally agree, we have them sign a cash4keys document. On agreed upon move out date, the PM inspects the home for damages. If anything is damaged or unclean, we have their signature on a document saying they agreed otherwise, so we ask them to remedy it immediately or pay the difference on the spot, at a later date or we take them to court later on.
Only after they've handed over the keys and signed the document do we give them a $250 check, which they have to endorse and cash, so we get double the documentation of a move out related payment.... so if they somehow "work their way back into the property" after we've changed the locks, we have 2 signatures proving they were paid to vacate the property.
Full disclosure: this has worked twice for me, but it did not proceed along the time scale we wanted. Tenants would say "oh sure, we'll leave by XYZ date" and they didn't do it. We tried to get them out in 30 days, but it took more like 60.
Only when we proceeded with eviction and tenants received judgment/eviction notices did they get the message. So my advice, start the eviction process, so they know you're offering both the carrot and the stick, but give them the cash4keys option as a lesser of 2 evils.