miwo
Your note about derivatives is why bunnyhopping is still technically possible in TF2. Because airstrafing is "non-holonomic," the increased total distance that comes guaranteed when you airstrafe translates into increasing or decreasing velocity and acceleration.
https://www.youtube.com/watch?v=VoarskhqnrA
This might also explain why w-strafing is "worse" than A/D strafing: An A/D strafe keeps acceleration perpendicular to a player's current velocity because acceleration in Source is based on the keys you're pressing. So by strafing with A or D while moving in some velocity through the air, total distance is increased because you're turning through the air at a different angle than where you're currently headed. And because velocity and acceleration also presumably depend on distance in TF2, increasing your distance pathway through the air increases your velocity and acceleration while in the air as a result.
A W airstrafe, on the other hand, keeps velocity and acceleration together for the player. This results in smaller-angle movement through the air (you can't rotate your velocity as quickly with a w-strafe than with an A/D strafe), and a kind of "pulling feeling" back in the direction of your original rocket jump. These smaller angles result in less gained position in the air, which in turn causes less gained velocity and acceleration.
A/D strafe, where the black arrow is velocity and the red arrow is your strafe key: https://steamuserimages-a.akamaihd.net/ugc/1100293836530956311/3F5B008BE5788665344963CE8A73B904DE20092A/
W strafe: https://steamuserimages-a.akamaihd.net/ugc/1100293836530780512/FA053FBC5D325CA33EC65B1D3C3C8026545DD1CF/
Some more info about airstrafing is here: https://steamcommunity.com/sharedfiles/filedetails/?id=184184420