I have highlighted the actual collection agencies for you. In addition, it is worth noting, you are missing the NGA, although NGA and NSA both fall under DOD.
The reason we have multiple collections agencies is multivariate. Firstly, at least three of them are based around their assigned discipline. The NSA has primary responsibility for
SIGINT, the CIA has the primary responsibility for
HUMINT, the NGA has the primary responsibility for
IMINT and
GEOINT. The FBI is a collections agency as well because they have the authority to operate domestically. So, for example, if in the course of conducing HUMINT operations against a target in (making this up) the country of Outlandia, the CIA runs across John Schmuckatelli, who is a US person who seems to be involved (for example) gun running back and forth between the US and Outlandia, the CIA would, upon the realization that Mr Schmuckatelli is a US person, cease collection against Mr Schmuckatelli and hand him off to the FBI, who would then own the investigation against him. It's worth noting that this serves within the IC as a sort of internal checks and balances - all of your capabilities and authorities are spread across multiple organizations rather than being housed under one roof - and those agencies, in the good manner of all government bureaucracies, jealously guard their turf. Even our DOD SIGINTers who are collecting in the field in actual combat zones technically have to listen to the NSA, because they "own" SIGINT. If you are a DOD Huminter and CIA wants to steal your source, too bad, so sad, you lose, because CIA "owns" HUMINT. I've never heard of NGA swooping in to try to control Geoint, but that is probably because NGA seems to be all retired DOD Geointers who are just enjoying life in a second career and like to be helpful. Asking "why so many agencies that spy", in a sense, is like asking "why have so many branches and levels of government"? Does it make us
less free that Legislative and Executive power are (supposedly, at least) not housed in a single body?
The DNI (Director of National Intelligence) is charged with overseeing the (often fractious, competitive, parochial) IC, and is an office that was created as part of the post-9/11 reforms when we realized that the intelligence to potentially ward off the attack was in front of us, we simply hadn't been organized to make use of it. NCTC (the National Counter Terrorism Center) is run by the CIA, and is a bunch of analysts, not collectors, who sit around and try to figure out A) what terrorist groups are doing B) what they are likely to do and C) opportunities where we might be able to stop them from doing so. They also help feed the no-fly list. Homeland Security (as near as I can tell) is a bunch of retired teachers and bureaucrats who are to ineffectual to assess their way out of a paper bag. They also don't have collection, but are dependent upon others for that.