It's the job of the master to pick a proper apprentice, and teach them the way of (and importance of) the rule of two. Like communism, it's good on paper but horrible in practice or real-world application. The rule of two pretty much died out at around the time of Plagueis. The Sith has to want to abide, and the master must test this and be vigilant. Cunning is a good thing to have in an apprentice. Patience and critical thinking and all that jazz as well. A Sith doesn't need to win the rule of two battle by using brute force, they just need to win and understand the importance of that winning.
Most think that only the apprentice initiates the challenge, but it's partly the master's responsibility as well (Sidious turned away from this concept, thinking that the apprentice was to be more of a servant rather than a student, and not coming to terms with his own mortality or staying true to the reason for the rule of two, for Sith to rule the universe again. Sidious made it about Sidious ruling the universe, and lost sight of the original goal, which is why the rule of two failed).
Anyway my point is that it's also the responsibility of the master to cull a weak apprentice before weakness or fatigue/old age sets in. The rule of two wasn't set up to be a necessary tradition (although Bane did contemplate that if there were only two Sith, the force may use them as it's only darkside conduits so-to-speak, making them that much stronger. This is proven to be false by pretty much any era of Sith history before the dynasty of evil though, where there are numerous very powerful Sith existing at the same time), but a means to an end. Bane saw a losing war, saw the Sith being lead to annihilation, and set up a clever plan that would've paid off had Sidious never been a part of the Sith order in the first place (he pretty much ruined the entire plan by trying to hold all the power for himself, the plan was set to rebuild the Sith empire, not give it all to one person. Bane considered how this could be idiotic and lead to the downfall of the Sith, and was one of the reasons why the rule of two existed in the first place).
I'm starting to get into other areas that are not my point though and just talking about whatever. My bad. My point is this: The rule of two was a beautiful plan for what it's intended purpose was: the rebirth of the Sith Order and the annihilation of the Jedi Order through subtlety, patience, and timing. It was basically the Sith run on a skeleton crew to avoid the Jedi while accruing the resources to strike, all with built-in failsafes to ensure that the plan is maintained (Sidious fucked this up, he shouldn't have been a pussy about losing his power and started up a proper Sith Order in place of the old Jedi Order) and the timing is perfect.
Good on paper. Brilliant for what Bane wanted to do. Terrible in practice. People got lazy and delusional. If you ask me, the wrong person was picked only because he was strong in the force and good at manipulating people. He was also kind of a dick and didn't fully understand why the rule of two was even a thing. He just wanted the win, he didn't want the reality of that win.