It provides an additional layer of security to those who are at risk for being sued for damages to other people's property or injuries caused to others in an accident.Just my opinion here. 

If my insurance does not cover me for certain breeds, why should the law require me to put myself and others at risk of injury or a lawsuit over an attack???

What legal trouble could I get in for injuries of unlicensed, uninsured handymen on the job?

They could sue for permanent injuries.

He said they would of course sign a waiver that I wouldn't be responsible for any injuries due to the condition of the home.

There isn't one person with a pet that will tell you the pet isn't perfect.. yet check here on BP and find out how much damage urine, chewing, yard damage, nuisance barking, pets cause let alone injury from bites and attacks. 

You take action and just state the nature of the complaint is such that the dog has caused personal injury that required medical attention and the dog has shown aggression and must be removed from the premises, immediately within 24 hours.I would go NO pets in the entire building. 

.), they had attempted to work with large lending institution to make payment alterations due to injury, (bank wouldn't) and would just love to put it all behind them. 

You really do not want to run the risk of getting something happening and you either A) get by under the radar of not driving for business purposes, but not having enough coverage to cover other's injuries or B) Not having commercial insurance on your vehicle and found out that you are driving for business purpose, thus no pay out. 

If you provide extinguishers you are obligated to provide proper training on it's use and in the event of a fire, where a tenant is injured attempting to contain a fire, you can be held liable.Better pray the extinguisher does not malfunction or the tenant does not use it improperly resulting in injury or death.