I could not believe some of the human debris showing up to look at the house. 

We are all human - you'll know better for the next one.

It is well established that in terms of human behavior, motivation will help you for the whole of about 3 days before you run out of it and you fall into a slump where's you think "what's the point?  

We would prefer to keep the human occupants to no more than 3 and pet applicants to no more than two. 

I may be misreading this, but from my experience of human nature and working with teenagers, if you see this young man as a "punk" or "jerk" and treat him like one, he'll fulfill that role.

I'm willing to go ahead and apply for it, it just seems so inapplicable and absurd.

Much like a business doesn't need to allow everyone into their establishment, however the moment you try to explain why, you'll be opening yourself to a whole bunch of possible human rights complaints.

Also, a reason not to accept a security deposit from a nonprofit or social service agency is because if you get into a conflict with the tenant, the organization will "advocate" for them, including legally, and may be quite absurd (and incorrect) about the level of "rights" they claim for the tenant, and this is super stressful, and also, now you have a very entitled tenant who thinks you're obligated to put up with all sorts of awful behavior- because they've been erroneously led to believe that they have excessive "rights."   

That kind of rent growth is one of the reasons why people buy apartments in that area for absurdly low cap rates. 

Just had an IRS audit with someone who took that approach - they got crushed.Remember the human element of the law - it is not just what is on the books.