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Someone (not me) should run an 'Ironman' Campaign where you get only one roll for stats and take any skills that you get with no alternatives. It would be interesting to watch.
Not sure what you mean, but when we started, that is exactly what we did - roll and it is what it is.
Which, as others have mentioned, left holes and senseless overlap of skills between characters, not to mention serious disjoints between characteristic stats and skills and, as you mentioned, odd skill combinations. And, of course, from many players' perspectives, very limited option to play 'the character they wanted'. This could, in turn, encourage rolling older PCs to get a desired skill set (and bump up stats).
Which, with the chargen waste mechanic, er, death, could be frustrating. Hence, there seem to be a lot of house rules and fudging in this area, not to mention dropping the death mechanic (and later editions provided more skill options, and, in the case of Mongoose, did eliminate standard chargen death). I had no problem with the death mechanic, on principle, but for players who weren't trying to be munchkins, it was a waste of game time.
In my CT games, after creating automatic char generators, players just used my NPC generators - which explicitly followed the rules ala 'Ironman' if you will. However, they picked from the resulting random list who they
wanted to play, instead of just going with the first thing that came along.
Since the chargen mechanics are so well balanced (CT creators knew their statistics), and my players weren't interested in playing comic book superheros anyway, this resulted in interesting and 'believable' characters.
It also nicely addressed everything I mentioned above.