I've removed the spoiler markup since the OP has read the series. Fair warning.
In chapter 15 of Ringworld's Children, the Pak protector Proserpina described how the Ringworld came to be. Of the flattened maps of various worlds she had this to say:
"Stars that can generate extensive planetary systems form in clusters. There were stars with planets around us where we stopped, and some were Pak-like or close to it. We identified those that might evolve dangerous enemies. We collected local ecologies and settled them on maps of their worlds."
This matches what Chmee deduced in The Ringworld Engineers:
Chmeee snorted. "Obvious to the meanest intelligence, Louis. It is a roster of potential enemies, intelligent or near-intelligent beings who may one day threaten the Ringworld."
The roster, laid out in maps on the Ringworld itself, was designed to provide information useful to an illiterate, newly awakened Protector. As maps with obviously transplanted ecologies, the information was presented in a way that could be deduced intuitively.
On the larger issue of why Protectors would permit dangerous species on the Ringworld, the maps have to be understood as part of an experiment undertaken by a large number of Protectors trying desperately to break the cycles of interstellar expansion and warfare that threatened to end their species. Summarized from Ringworld's Children, this group of Protectors set out to do two things: 1) separate themselves from the rest of the Pak race, and 2) breed out the monomaniacal and xenophobic traits that made them a menace to themselves and incidentally to every other living thing not immediately beneficial to their breeders. They built a cylindrical ship ala Rendezvous with Rama containing an ecology, their breeders and themselves, with the breeders completely walled off from the Protectors. The penalty for any direct contact with breeders was death. Some breeders died without their Protectors to help them. Some Protectors stopped eating because they felt purposeless without contact with their breeders. Some Protectors tried to sneak into the breeder section of the ship and were caught and killed. Eventually, as Proserpina described it:
"What emerged at the end of three hundred and fifty thousand falans of travel, was a race that can live without the smell of our own blood line constantly in our nostrils."
The surviving kinder and gentler Protectors then constructed the Ringworld and tried to run it under the same model of governance, with Protectors and breeders strictly separated. Protectors who violated the rules were killed or imprisoned with a sampling of their breeders, with no technology that could disrupt the status quo.
According to Proserpina, these early pioneering Protectors could have seized all the worlds of Known Space, but their ambitions were greater than that. Instinctual conquest and slaughter were the traits they were trying to breed out of themselves. So they built the Ringworld and sequestered themselves there.
The enforced peace lasted for a long while but all things end. Fighting broke out among the remaining Protectors, with an eventual victor or victors controlling the Repair Center. But these victors did not feel the urge to slaughter all but their own bloodline. So the wild mutations among the humanoids into various ecological niches and the map worlds of aliens were allowed to grow and develop unimpeded.