It's not an easy problem to solve, but it is not unsolvable.

I don't think 'solve' is binary. Different solutions come with different tradeoffs. Membership of supreme courts is made up by judges chosen by political majorities. There are advantages to having a powerful fourth estate that's independent of the other three.

As a practical matter getting a parliament to pass legislation that introduces a new class of people that check whether or not the members of that parliament are holding their promises also seems unrealistic.