I'll have to think about why the Shi'ar don't bug me the same way, though.

I would disagree and say Unus and even The Blob were credible threats. Those were situations that really had the X-men on the ropes. Lucifer even was intimidating and seemed to be a real challange for the team.
The later developments for those characters weakened them, but they were great villains during their introduction. Don't forget, characters like Doc Ock didn't reach greatness until their second or third appearances.
If Thomas didn't make Lucifer an Alien, or Unus didn't fade into obscurity, the villains could have stood the test of time.

Not to hijack your post, John, but I did want to bring up something from the Morrison NEW X-MEN thread that I think bears mentioning here: Claremont's most important change was to the metaphorical engine (it's also his most overlooked one). The Lee/Thomas X-Men were freaks, teens rejected from society but told to protect it by their bald dictator. From a feel-your-pain reader perspective, that's not an easy metaphor to tap into. But Claremont's X-Men were rebels, not so much rejected by society as they were mistrusted by it, but driven to protect it by an innate sense of being a part of it. It was a very slight, almost imperceptible adjustment, but one that allowed Claremont to tap into general teenage metaphors that his predecessors couldn't. The "freak" angle didn't disappear, it just applied to mutants in general, not the X-Men specifically--and in doing so, allowed the X-Men to seem less freaky and more "relatable" by comparison. This in turn freed the X-Men from the Dr. Strange-type pulpish stories and into the more superheroic action-adventures.

As for the "Why keep the X-Men name?" question, I'd guess that it was because of the mutant connection. Wein and Cockrum, I believe, were just working on some generic team--not necessarily mutants--at first, but it quickly became apparent that Cockrum's Storm/Black Cat, Colossus, and Nightcrawler concepts fit the mutant mold pretty well. Then when Wolverine made a splash, it sealed the deal for a mutant team. Sunfire and Banshee were from X-canon, so I think that led them in the direction of calling the team X-Men. With Cyke as leader, it became apparent.

I do think it's admirable that the originals didn't fade away, though. As individuals, they are just as much X-Men as their more popular ANAD teammates. Hell, when they were X-Factor, even the X-Men themselves thought they were the real X-Men. And look at the movies: of the 12 characters who could be considered X-Men, HALF of them were originals (including Charles)! So I guess it's a good thing Marvel DIDN'T decide to name the ANAD team something else...

I've always thought that there are some superheroes who have been kicking around for years and STILL haven't "clicked" with the right creator who could really make them work. Aquaman's an obvious example. But you know who else I'd say was like that? Iron Man. It really seems like he has the potential to be a major league character--he is in the Marvel U., of course, but the average joe has barely heard of him--yet despite a couple of interesting hooks, alcoholism especially, I feel like no one's ever quite opened up the character to his full narrative potential. Maybe the movie will change things.

Still, the original team had a lot of promise that still hasn't been fully realized ( credit goes to everyone who's tried, such as the Simonsons on the original X-Factor, or Jeff Parker and Roger Cruz on the current First Class ).