As for jump button, we've seen plenty of aerial combat. I presume the jumping happens when it's need in the combat. The only difference is you can't just jump around the place like a kangaroo.
From video that I've seen the aerial combat that I've seen looks cool, but it seems canned and executed with pre canned button presses. Some part look like a QTE style from Shenmue.
HS will probably have attacks that launch enemy into the air and you have option to follow them up for aerial combo without needing jump button.
In DMC3, jump button play other role other than to jump around like a kangaroo. But I like to make my avatar jump around like kangaroo.
For the DMC3 I like the use of jump button for enemy step (using enemy grounded or in the air as platform). Without jump button, you can bring Dante into the air, but he won't stay up for very long, several slashes/attacks and he'll be back on the ground, he gets more slashes/attacks if you cancel and reset those canned animation. But with enemy step and its canceling properties, he can stay up in the air for aerial combat, till the enemy dies.
DMC3 is a more interesting system that way, than if I just input button presses for all the aerial combat canned animation to finish off the enemy. Even if you can cancel and performed different variety of aerial animation, the character staying up in the air, is not your skill/control, but pre canned.
Furthermore in these sort of games, I like short chain if there are pre canned chain of attack compare to long pre canned chain and moves are accessible individually rather than having to go through the pre canned animation set that the moves is part of. As long as each move has unique property that separate them from the others and you have some way of canceling them into each other, it'll be a more interesting game to discover you own chain in an intuitive way, compare to thousands of pre canned animation sets/attacks that you have to remember the chain of button presses for.
Its even better if canceling method that require tight timing, rather than loose timing, this way my hands and eyes won't get bored. If it is loose, I'll group it into button mashers.