I can't speak for Europe / England and their repair laws, but everything in America is required to be approved by the FAA for use in aviation, and usually you can't change things after the aircraft is certified
In theory, you are correct.
However, in practice, you are completely wrong. Uncertified parts are everywhere and in the 70s/80s, a huge scandal arose because counterfeit parts were found all the way into Air Force One - the aircraft part supply chain was full of counterfeit or uncertified components that it made its way onto the most secure aircraft in the world. The FAA cracked down heavily, but it happens more often than you'd think.
NorthridgeFix has a series of videos where they repaired a Cessna icing controller circuit board, and they got a visit from the FAA. The FAA said everything he did was legit, but they wanted to look into his customer to make sure they were properly certifying parts because people still put cheaper counterfeit (uncertified) parts in. The circuit board he fixed may cost only $300 or so in parts, but after certification and documentation it's probably at least $10,000.
And the FAA notes there are exceptions to the rules - privately operated aircraft well, they have far less oversight. Even the FAA admits it. It's only when transactions happen do they start getting involved (i.e., you sell an aircraft with uncertified parts in it).
Finally, there is also the homebuilt exception - not all aircraft are certified. You can certainly build your own aircraft, and the rules are really lax in that regard - as in, you are pretty much free to do whatever you want.