What problems with the other tenants (who they likely know well) could they cause?

And they’ve cost me alone well over $30k in damages and lost rent thanks to their complete negligence.

Lenders desperately need/want business especially in this interest rate environment (right now, the main source of mortgage loan business in Florida is rehab financing as a result of the hurricane damages) and one way the big players differentiate themselves is by streamlining the process.

I would only ever consider this if the ceilings are already falling down or damaged.  2.

This caused a historically unique opportunity for investors - they could buy Class A properties and immediately cashflow when renting them out.This couldn't last forever, and it didn't, as excited new investors drove up prices.

Fortunately, we have not had any issues on the property that were caused by any pet. 

Only caution is if they don’t have checkbook control and there’s a time crunch going through the custodian can cause delays and red tape to deal with.  

There i a bit of research that needs to be completed early on in order to get a good judgement on the feasibility of this; from there, the "Official" way to ensure you could pursue this would be to request a "Zoning Opinion Letter" to receive an Official decision from the Department of Zoning in order to ensure this will not cause any issues during your permit review. 

@Joe Gellenbeck Recommend you first figure out the property Class you want to invest in, THEN figure out the corresponding location to invest in.Property Class will typically dictate the Class of tenant you get, which greatly IMPACTS rental income stability and property maintenance/damage by tenants.If you apply Class A assumptions to a Class B or C purchase, your expectations won’t be met and it may be a financial disaster.If you buy/renovate a Class A property in Class D area, what quality of tenant will you get?

Give them notice if their pets cause any infractions they will need to be removed in 24 hours.