Agreed.
I always preferred games with delayed response, no air control, and better jumping anticipation, animation & feeling.
Today, nothing has changed, and there is still two ways of designing a game. It's called "body awareness", and some people prefer FPS with instant response like Quake, UT, L4D, COD, where you feel like a floating camera, usually you don't see your feet and the ironsight is extremely fast, and some others prefer FPS with body awareness, slower ironsight, slower turn speed, progressive acceleration, games like Killzone, Arma, Mirror's Edge, etc.
So basically it's a question of game design. Is your game fast-paced, and does it relies on jumping all the time, with short reaction times and a great landing precision ? If yes, if your jumps need to be precise, then go for a free jump mechanic, allow air control, and let the player jump instantly and land exactly the pixel he needs to. The animation is purely graphical, it's not tied to the gameplay. This is typical Japanese game design. This is like Mario, Sonic, Megaman, Devil May Cry or even Uncharted. If not, then prefer a predefined jump, with anticipation, that need to timed and planned, where animation & gameplay are really linked. This is typical occidental game design. This is like Flashback, Abe's Odyssee, or the old Tomb Raiders.
Make your choice.