The Collectors have been around a long time as a minor thing, but if entire colonies start vanishing then that is more than enough for a Spectre to hop on the job as a possible galaxy wide threat
Cerberus were the only ones we know of who were actively investigating the situation and trying to discover the culprits and even they didn't know for sure it was them until Freedom's Progress. The issue clearly isn't that important to the spectre's since we don't hear from any other spectre searching for information on the subject. Cerberus and Shepard seem to be the only ones taking the collector threat seriously, yes, but at the time they were the only ones who really knew it was them.
The Council are just d*cks for claiming it's just a human-problem. Hey Council. Entire colonies are vanishing to an unknown alien aggressor. You'd think that would at least get your attention to investigate things. Same goes for the Systems Alliance.
The missing colonies were all outside council space. They don't guard or protect colonies placed outside their boarders, its part of the dangers that come with colonizing worlds in the terminus.
The Alliance were clearly doing SOMETHING. They sent Vega's team to protect one colony (Fehl Prime) in the terminus and plus they invested in the defense towers on Horizon. They just had no actual evidence at the time that the collectors were the ones behind the missing colonies. I don't blame them for assuming it was pirates - the batarians especially have a nack for this sort of thing. The terminus is a dangerous place.
IMO, prior to the events of Horizon or Fehl Prime (whichever happened first), neither the alliance or the council had any reason to assume the missing colonies were due to anything other than pirates and slavers. I'd sooner believe it was the batarians responsible for it rather than think it was some mysterious species that the majority of people believe are fictional boogeymen.