I'm with Christian on this. Angel, Iceman and Beast are iconic, first-generation Marvel characters for me.
If they've sucked for you up to this point it's just that... well, they haven't been handled particularly well in ANY medium to date. All they need is a bit of TLC to bring them to life.
You could argue (Quite successfully I think) that Marvel Girl was in an even worse position than them for the first 15 years of her publishing history. But all it took was one writer (Chris Claremont) with the will to put things right, and today Jean Grey is one of the best known and best loved characters in the Marvel universe.
One good writer (Or producer, or director). That's all it would take.
And I certainly wouldn't call the original X-Men the biggest failure of 1960's Marvel. Sure, they weren't Marvel's biggest selling title, but they did better than Ant-Man/Giant-Man, The Human Torch solo feature and even initially the Hulk. It's doubtful whether Doctor Strange and SHIELD could have supported their own titles for as long as X-Men did back then.
And X-Men only got cancelled during a wave of Marvel cutting back on it's lower-end books. Doctor Strange, SHIELD and Captain Marvel all got the chop in late 1969, while X-Men and Silver Surfer lasted a little longer, through mid to late 1970.
AND, X-Men was immediately revived as a reprint title that lasted 28 issues (Right up to the revamp in Giant-Size X-Men #1). The only other title to be given ongoing reprint status was SHIELD. and that lasted... three issues.
Beast, perhaps, but Angel and Iceman are irrelevant to everything about the X-Men. Period. There's nothing whatsoever iconic about them. You don't see Avengers movies including members like Swordsman, Hellcat, Starfox, etc. Angel and Iceman are to the X-Men what these characters are to the Avengers.
For the past 55+ years, Iceman had one single important showing: OZT. That's it. Nothing before. Nothing since.
Angel got important when Apocalypse twisted him. That's it. Nothing before. Nothing since.
But neither of these things are very important to the overall X-Men story. Both are easily done by the vastly more important "second genesis" X-Men characters.