The philosophy behind the rule of two is that the greater power triumphs, before it was instituted there was a problem where dark lords were defeated not just by apprentices that had surpassed them but by multiple apprentices banding together temporarily so they may strike down their master.
This leads to a net loss in power for the Dark Side, so the economical thing to do would be to come up with a system where the Sith Master is only discarded when somebody stronger arrives. Or, to quote the relevant book:
"When your power eclipses mine I will become expendable. This is the Rule of Two: one Master and one apprentice. When you are ready to claim the mantle of Dark Lord as your own, you must do so by eliminating me."
―Darth Bane: The Rule of Two
This by no means excludes other dark side users from existing, but the underlying assumption (which in the end is really quite arrogant) is that the only person who might possibly hope to take down the Sith Master is his or her own Sith Apprentice, anybody else would be too weak especially since the Apprentice would defend his Master.
No, somebody who wants to be a Sith would instead go after the Apprentice, in the hopes that killing him or her they can impress the Master enough to become the new Apprentice.
The lethal competition that is so crucial to the proper functioning of the Dark Side / Sith continues, but the knowledge possessed by the Master will generally be transferred to the next generation.