We focus primarily on what hazards does the work the person does introduce into the home.  All our home workers are home working clerical work on computers.  This doesn't (reasonably foreseeable, in my opinion) introduduce hazards into the home that the provision of a first aid kit or having goine through first aid training would mitigate.  That is, focus on foreseeable hazards arising out of the work activity.  I'm much more worried about posture and suitable workstations than I am about bandages, slings and CPR training.

We don't fisrt-aid-train every employee who works at home.  Nore do we issue them first aid kits (nor, for that matter, do we issue them fire extinguishers or install fire alarms in their home).

I note HSE guidance aimed at home workers: "If your work is low-risk, such as desk-based work and you work in your own home, you don't need any first aid equipment beyond normal domestic needs." (https://www.hse.gov.uk/simple-health-safety/firstaid/first-aid-home-workers.htm)

I further note that HSE guidance clearly anticipates that even a non-home workplace with multiple workers  might conclude that no trained first-aider is needed (again according to HSE guidance) "As a minimum, a low-risk workplace such as a small office should have a first-aid box and a person appointed to take charge of first-aid arrangements,such as calling the emergency services if necessary. Employers must provide information about first-aid arrangements to their employees.  Workplaces where there are more significant health and safety risks are more likely to need a trained first-aider."  (https://www.hse.gov.uk/firstaid/index.htm)