But I've never been challenged on it and my attorney doesn't seem too worried that I'm abusive about it, so I still have it in my lease that criminal activity - even without a conviction - may be grounds for termination.

There are also really bad neighborhoods where you can find islands of super nice, clean, housing with very few criminal elements on the block.

@John Thedford can quote chapter and verse of FL laws on the topic along with a list of people who have been prosecuted. 

They need to go to jail and people need to STOP doing illegal AirBnB.If you really want to make it legal, then lobby the Governments to make that change so ALL OF US can make money..... not just the criminals.

If they are embezzling money and there is proof talk to the DA if you want criminal charges, or take them to court with a lawsuit if you want money and a judgement against them.

Does this standard apply to low income areas where many tenants may have criminal backgrounds?

Not complying is illegal, and there are criminal penalties like jail.

Re: Rental application expenses... not only is there an out-of-pocket expense to run online credit history, criminal background, and rental history checks, but many times there is additional time/effort in manually verifying information.

Because I'm the one who wants to know about their criminal/credit/eviction record. 

application fee that will do a credit, criminal, and eviction report, which is great as well.