Your unlicensed contractor or handyman does not have workers compensation insurance. If the work requires a contractor's license, and your contractor doesn't have one, then you are the direct employer of the contractor and each of her employees. If you, the property owner, do not have workers compensation coverage and workers compensation insurance is required by law, then the Labor Code imposes a rebuttable presumption that the "employer"/property owner was negligent. Since you the homeowner were not actively managing the work, especially safety procedures, overcoming the presumption is unlikely. There is no insurance coverage, and there is no monetary limit to the damages which can be awarded to the injured worker!
If an employee of an unlicensed contractor is injured and worked on the property for less than 52 hours during the 92 days prior to the injury, then there is no workers compensation coverage, by law. If the injured employee worked inside more than 20 hours per week or outside more than 10 hours per week, the homeowners policy probably does not provide workers compensation coverage for that employee. The exact limits vary from policy-to-policy. Your general liability insurance also will not cover an injury which is supposed to be covered by workers compensation. No insurance.
Work for which homeowners sometimes hire unlicensed contractors, which require a license, include roofing, painting, tree trimming, and installation of carpeting, linoleum and wood flooring. Such work produces disabling falls, broken bones, and back strains and injuries.
Besides that risk of potentially crushing and bankrupting liability, a licensed contractor is more likely to have the training, experience and professionalism you need to get the job done correctly and safely.
Are licensed contractors more expensive? Of course they are. They pay for insurance. They pay market wages for their labor. They pay license fees and taxes. Is it worth it? Always.