Some people are more into gambling than others, that's all.

Had to pay a premium cost for the service, but other than that, no skin off my back and both times the tenants were thrilled that I got it taken care of so quickly on a holiday weekend. 

The issue is that I would gamble they will not pay via money order to your P.O.

However, the thrill is gone and they will be soon. 

And they're often thrilled to have the key in hand, so they can just show up when they get there the next day. 

There will still be some who apply who have a reason for automatic denial - they are willing to gamble that the landlord won't check them out ...But the answer is still yes - that way you are operating in an ethical fashion; those who have a reason for automatic denial should recignize that they are better off going elsewhere, and if they don't they can't say you never told them up front about why they would be declined automatically. 

He was thrilled!

I'm sure it can be more difficult in the winter months as most people aren't too thrilled at moving when it's 5 degrees outside, but I haven't had it happen to me personally. 

We are inheriting our tenants, which we aren't thrilled about.

That's on them.Your tenant sounds like someone with a gambling problem.