The idea that Palpatine is illegitimate because he somehow failed to follow the Rule of Two is ridiculous.
If Palpatine wanted a weak apprentice who would never be able to replace him, why did he replace Dooku with Vader? Why did he try to replace Vader with Galen Marek and Luke Skywalker? The simple reason: He actually did want a powerful successor. He was very much aware of Darth Vader's potential and based on what he said to Yoda, fully expected Vader to win. Didn't he tell Yoda, "Darth Vader will become more powerful than either of us?"
After Vader's defeat, Palpatine spent virtually all of his spare time trying to find someone better and eventually decided on Luke Skywalker.
Last time I checked, Darth Bane never destroyed the Republic or ruled the galaxy all by himself.
Also, the one and only goal of the Sith is to destroy the Jedi order and establish Sith rule over the galaxy, not to secure a good apprentice. Finding yourself a good understudy is just a succession device used to ensure a smooth transition of power from one Sith lord to the next. If anything, the Rule of Two is just one part of the master plan of the Sith to take over the galaxy.
The only Sith lord who has ever truly fulfilled the ultimate goal of the Sith is Darth Sidious, who ruled the entire galaxy for two decades. No Sith lord has ever wielded as much power.