The point that needs to be grasped, and put in a very general way, is that providing 'services' to 'clients' creates a legal relationship between the parties, even if not a business or commercial one because no contract is involved. The essence of a business contract is being paid or receiving any other "considation" for doing or providing something. Liability can also arise without a contract, like a car accident involving unrelated drivers.
When things go wrong, as they sometimes do, situations can lead to a claim against the provider which is where insurance comes in, hopefully.
To try to stop things going wrong in the first place, legislation has put in place a lot of "compliance" intended to stop unqualified people getting themselves into risky situations. For example, you need licence to drive a car, medical registration to work as a GP, and professional qualifications and appropriate work experience just to lay out cones on a highway or dig up the pavement.
Another of those compliances involves the CQC to regulate providers of "care". This isn't going to go away for good reason, so just get over it.