Jumping relies upon strength more than coordination? Long jumpers and high jumpers rarely compete in power-lifting. I think acrobatics is a good idea, just look at the floor exercise in gymnastics. While they both use strength, Swim and Climb aren't related closely enough to logically combine them.
Actually, I would disagree with you about the jumping. Long Jumpers and High Jumpers exert an enormous amount of strength. While it isn't power lifting, jumping in such a degree actually exerts more energy than "power lifting" does - requiring more more strength. I think Jump and Climb should be one skill (call it whatever) and be STR related (I'm sure theres been many a posts on this, but I happened to read yours here and haven't seen the others). I agree with you on Climb and Swim though, I think swim should be its own skill.
The class is called "Fighter" not "Single Weapon Specialist." Any Fighter is a doofus who doesn't train off-handed, with and without armor, sober and drunk, unarmed and armed with as many weapons as he can. You train to use them so you can fight better against them with the weapon(s) you prefer.
The Fighter does all this training while the spellcaster is learning his runes and lore. It's what makes him a Fighter and not a dude who picked up a sword and decided to go adventuring.
As you point out, there are still have weapons you prefer to use. An argument that you're as good with the things you don't use as you are with the things you do doesn't inspire me to think about how realistic this is. I preferred the system of weapon groups from 2nd edition myself, since there is overlap between different weapons but you could still be specialised in one.
Whoah, there. Back up. The point is that in 4e all classes progress at the same pace, Level/2. The Ftr should indeed be far better with a weapon "he doesn't use" than a Wiz would be with a weapon he "doesn't use." And, in fact, the Ftr might be better with the non-preferred weapon than the Wiz who uses that weapon preferentially, unless that Wiz has invested something extra in his weapons training.
Whoah, there. Back up. The point is that in 4e all classes progress at the same pace, Level/2. The Ftr should indeed be far better with a weapon "he doesn't use" than a Wiz would be with a weapon he "doesn't use." And, in fact, the Ftr might be better with the non-preferred weapon than the Wiz who uses that weapon preferentially, unless that Wiz has invested something extra in his weapons training.
We're going to have to disagree here. As far as I'm concerned if you have a fighter who has never used a flail, say, and wizard who has also never used a flail then the difference in terms of how well they use the flail is going to be insignificant.That's the point: no such thing as a Ftr who has "never used a flail." He's trained for months with every weapon known to his native culture on the way from "guy who picked up a sword" to "Fighter." He can't carry around one of everything, but he knows full well the use of everything and anything that might come to hand.
The fighter may have an advantage from being physically more adept, but that's reflected in their STR/CON/DEX stats. He/she may have an advantage in knowing tricks about avoiding blows that the wizard doesn't, but that's shown with hit points.
But not in BAB? The guy who practices "fighting" every day, while the Wizard is muttering over his scrolls and books, isn't just plain better at it? Is there a rule that Ftr must have better STR/CON/DEX than a Wizard?
BAB isn't how to attack with a certain weapon but not another, it is how to attack, period. It is how to control the distance between you and your opponent, and practice in spotting the opening and darting in to strike with minimal vulnerability to counterattack. Whatever the Wiz knows about fighting he simply doesn't have time to practice the way a Ftr does.
I'm not arguing that a fighter shouldn't be better with the weapon they use than a wizard is with whatever they're using, or that a some weapons aren't similar enough that some of the skill factor carries over, but I really dislike (and changed in my games of 3e) the concept of universal proficiency with all (almost all) weapons for several of the classes.
I think you have confused proficiency with Specialization/Focus, which are separate Feats in d20.