My initial thoughts are if you see them and then deny them a discriminatory issue may arise so you better have another reason. 

When tenants stop paying for utilities other problems arise, such as burning candles for light, using propane devices for heating, and BBQs for cooking, running extension cords from other residences and overloading them, and in the winter, freezing pipes.... to name a few.

@Joe Splitrock I think I will hire a cleaning service in the future, especially when situations like this arise. 

It's one thing if unpredictable events arise and your put in a bad spot (I almost always waive the late fee in this case), but it's another issue entirely when tenants don't pay on time because they don't see it as being important, they think 'he's a landlord, he's rich, he can wait,' or any other variation of this moronic line of thinking. 

You deal with problems that arise from it -- domestic violence, noise complaints, drama.

I wonder what are the potential issues aside from difficulty renting that might arise from having a basement apartment on a property zoned SFH?  

We suspect this increase arises from the convenience of having en-suite laundry leading to tenants doing more small loads.Including en-suite laundry is not a matter of our units being hard to rent (they are not), but part of our business model to offer better value than our competition .... we similarly carry out deep energy retrofits of properties we acquire and have found the extra renovation costs up-front lead to less and quicker turnover.

Read your owner's policy, it probably excludes coverage for other risks arising from contractors, managers, employees or others, when other types of coverage are available in the market, that coverage will be required to be the first covering specific exposures.If your PM is negligent and causes a claim your owner's liability kicks in protecting you, that coverage will "subrogate" against the PM for damages as to their professional liability.

If a situation arises where you need the funds, you will have them.

I would suggest contacting a local tenant's right advocacy service if this arises as most tenant fail to follow the proper steps in this regards