I think the lack of a mechanism for the ability makes perfect sense in a storytelling game. For those using the game system who are not wishing to play a storytelling game then there are issues.
I wouldn't say I play a "storytelling game." Yet the lack of a "mechanic" for that part doesn't bother me. The reason is that I just don't need/want a rule or a die role for every conceivable action or part of an action. That road gets way to cumbersome for me, and doesn't help me in any way. Just give me the abstracted idea basically and I'm happy.
If, as the DM i find CAGI (or any rule) to be disruptive, or harmful to our gameplay in some way, I will override parts of it as needed. The same is true for monster abilities, as I'm not playing against my players. I'm the neutral ref between players and the challenge.
Oh, I don't argue that 4e "isn't D&D", and I don't argue that there is no relationship between (say) 1e and 4e. If you believe otherwise, please point out to me what I said that made you believe so.
I am talking only about one specific change to the implied setting of the game, from TSR-D&D to 4e.
This statement is part of what makes me believe what I said. It's not a change in the "implied setting." D&D characters have ALWAYS been able to do this stuff. (In fact I think it's closer to how it was originally when D&D characters were indicated to be more then the common person.)
It's a world where heroes fight monsters, and even "non magical" beings/characters can do things above and beyond what normal people can/should be able to do. It's a world of "larger then life heroes and villains" where physics only need apply at the VERY most basic level. It's a world where archers can split arrows because they're THAT good, and things like wood grain have no impact. It's a world where Conan can bend metal bars with his bare hands, or fall off a cliff and survive. It's a world where men with swords can somehow defeat creatures 10 times their size without first having to somehow get to their level, or hamstring them somehow. It's a world where there are countless creatures stronger/faster/better then humans yet still we somehow seem to be on top.
And it's a game system where "games should be fun not work," and certain things are just left to approximates rather then endless strings of rolls, charts, and tables. It's a game where Conan survives that cliff fall because he had enough hit points, but the players add in things like "you manage to grab on to the edges, and to the weeds just enough to slow your decent and survive the fall."
It's a world where the fundane replaces the mundane. It's fantasy, same as it ever was.
Sure the rules have been changed to achieve what the designers hope to be a better/easier/more fun play experience. In my opinion they achieved their goal overall. You might (and probably do) disagree.
Maybe I misunderstand your point though. What IS your overall point?