A couple of points.
1 - I don't believe any type of motorised transport operation carried out for Hire and Reward (i.e. you are paid to do it) is allowed on a basic licence. There is always extra qualification. While a mini-cab driver doesn't need to pass an additional driving test, they and their vehicles are additionally licenced. (I believe there are successful prosecutions of people with basic driving licences driving licenced minicabs even when the minicab was off duty). In aviation, it works the same. You need additional training (mostly in knowledge) to be paid to operate an aircraft. This type of operation would be photography, pipeline patrol, traffic spotting, etc. (i.e. no passengers of freight being carried)
2 - To carry passengers or freight for gain (i.e. Public Transport), not only does the pilot need to be trained (a CPL) but the aircraft must be maintained to a specified (higher) standard and operated within a structure designed to ensure a higher level of safety (an AOC). Not withstanding any views about the AOC just being a piece of paper, the facts would suggest that AOC operations have a substantially lower accident rate than private ops.
3 - The 'trial lesson' structure is sometimes used to get around what would be an requirement to have an AOC if undertaking a pleasure flight. the logic is, you have chosen to give flying a go (you personally flying the aircraft) you know it is not a commercial flight with the service and safety you would expect - therefore complying with the full details of an AOC is unnecessary.
The whole purpose of the law is so ordinary people, who have no real knowledge of the risks and decision processes involved in running air transport are 'guaranteed' a safety standard that is comparable to what they would expect from any other form of public transport (i.e. very safe) and do not need to undertake their own due diligence. The law assumes pilots, flying club members and their invited friends have sufficient understanding of the risks, aircraft, and pilot experience to make these judgements on their own - and due to the lack of any payment, understand the operation has no guarantee of any given level of safety.