To everyone making claims about why people play Halo or why they like it or what it's good for, I'll just say the story can be pretty involved, even if over half of it is in the novels and other non-game sources, and there are fans that love all of it, and fans that love some of it, and fans that don't care and just love it because it's really fun, and fans that play it mostly for the story, and even fans that made a website that says, nominally and not seriously, that Halo: Reach isn't canon to draw attention to how think the story has been harmed.
Anyway, that's one of the nice somewhat unique things about Halo, sure it's shooting aliens in space (SPAAACE Space space space) but they aren't all faceless, even the ones that are actually part of a hivemind (though less so), and it turns out they aren't evil, and they don't just want to take over or destroy us and our homes because they felt cranky that day. As for the Spartans, that is to say, the successful participants in the Spartan-II and Spartan-III programs, the sameness is on purpose, for a variety of reasons-- there aren't a lot of civilians shown in the series but the ones that are are pretty different from each other.
The whole societal thing or whatever you want to call it, that's kind of the point, in Halo 2, though unfortunately not any of the others, the motivations for the Covenant are explored pretty well, and first contact with the Covenant, as shown in the novel written not by an outside author but the guy who does the stories for the games, was diplomatic and tried to continue that way, the Covenant were the first aggressors. The Conversations from the Universe booklet that came with the limited edition of Halo 2 is a pretty good source too, it shows an Elite that respects humans and thinks they're worthy of consideration for joining the Covenant, and of course by Halo 3 they've joined forces-- I think Hood's speech at the end of Halo 3 sums up a lot of it well, where he talks to the Arbiter, "I remember how this war started. What your kind did to mine. I can't forgive you. But... you have my thanks, for standing by him to the end," after which they shake hands.
As mentioned above, we're talking about video games here, there are hardware and software restrictions and matters of aesthetics, having more types of enemies to deal with is generally more fun, and the Spartans are partly so similar because it saves on disk space and memory to load the same things and use them over and over-- this would be the point where I point out Noble team, for all their faults, are at least varied, and are different people, and have somewhat different armor and gear to top it off.
Also the blue eyes thing may in fact have subtext but not what you think: blue is kind of the color of the Halo series, that Spartan's armor and that of another on Noble team are blue, the logo is (generally) blue, Cortana is (generally) blue, some of the Covenant's weapons are blue and most of the rest of the Covenant's stuff is purple, which is close to blue, Grunts have blue blood, and a lot of the tiny lights on Forerunner architecture are blue, not to mention the gas seen stored in Halo 2 and the power storage devices seen in various Forerunner places in Halo 2 and 3 glow blue.
There's one more thing, and it's more of an issue, the Covenant forces aren't exactly a slave army, the Engineers are pretty much forced to comply and the Drones are in a situation like blackmail or ransom, the leaders of the Covenant keep their colonies and queen in good condition, and the Hunters realized they couldn't win the war they were fighting against the Covenant and joined them and have a lot of respect for the Elites, but the Jackals are pretty much doing it for money, and the rest of the races are trying to recover Forerunner stuff to reach salvation through a poorly-understood "Great Journey", and will eliminate whatever stands in the way of that.
As a bit of an aside, also in the extended fiction although does show up a tiny bit in Halo Wars and Reach, humanity isn't as united as you might think, the whole reason the Spartan-II program was created was to put down human insurrectionist rebellions, and as was said in the video the making of Spartans isn't always shown as being the noblest or most moral thing to do.
This Movie Bob guy and Yahtzee both act like they know the Halo story probably because people have pointed stuff like this out to them and then they miss these things that indicate they don't know it, obviously they looked into it a little bit and that's nice but it's clear to me they're bluffing a bit and that's pretty frustrating.