The alternative is to have both the sole trader and the company, and give the customer the choice
Absolutely and that is how it is going to be.
One has to remember that when you need your Gas Boiler repaired, you can either ring Big Plumbing company (Ltd) or you can ring Mr A Plumber (Sole Trader).
However, as far as you are concerned the only difference is in the name because they will both have everything they need to satisfy the requirements to be on the Gas safe register (formerly known as CORGI registered).
If as a customer you were aware that Mr A Plumber was not quite up to the minimum approval standard of Big Plumbing Comapny Ltd, would you trust your life and money to that individual (and purchase a lot of carbon monoxide detectors with what money you may have saved)?
Everyone has recognised that one can not provide effective flight training out of the boot of a car - where do you do the pre and post flight briefings, where are the strudent records stored and using random aircraft from various entities that may or may not meet the appropriate requirements.
It is good for the customer that no matter if they obtain their training from a stand alone instructor or a big training school, they can reasonably expect that they will receive the required training to the required standard at a suitable aerodrome in a suitable aircraft and that there will be the appropriate facilities for briefings, planning and study of relevant documents. They can also reasonably expect that their training records will be stored correctly for the appropriate time.
Are people trying to avoid any of these important points? No? Then where is the problem?