There is, of course, a solution to this. Ban regulatory bodies from running their own competitions. EUFA would let a contract to a commercial company to run all aspects of the CL etc. including eligibility, prize distribution etc. UEFA then would concentrate solely on governance. UEFA, FAs, leagues and clubs could make representations but decisions would rest with the competition agent.
Not perfect, but better.
Secondly, active officers of clubs would not be allowed to serve on the regulators bodies. These ppl should be drawn from countries' FAs., and independent lawyers, accountants etc.
The EU could bring in a directive to force the issue.
Alternatively, UEFA could run their own comps with an entirely independent body as regulator.
Of course, it will never happen.