The thing about speed in games, I think, is that you need to be able to go faster than usual, but that it shouldn't necessarily be easy. With JJ2 you can always go at full speed, you're never going too fast to see what's coming, you can never go faster than that maximum (not while being in control, at least), and there's very little reason to slow down.
I've never thought of JJ2 as a "fast" game, unlike JJ1, which feels fast but very hard to control.

The main other games that come to mind for going fast are Sonic games (surprise surprise) and Dustforce.
I'm talking classic Sonic here, not the newer stuff. Sonic Unleashed is fast, but it feels more like a twitchy obstacle course that moves on its own, and not like it's moving that fast because you made it so.

I'm not really going to ramble about Sonic because most people already know the deal there. Dustforce shares with the classic Sonics a physics engine that lets you move quickly if you take advantage of the environment. Both also have their share of easy, almost cinematic parts, and each has some kind of supplemental mechanics to encourage speed.

The physics behind Dustforce are quite simple. Your usual platformer fare, with walljumping and stuff, but the 2 important things are a dash and a stomp. The dash lets you go at "full speed", essentially JJ2's run button, letting you gain momentum quickly, but not past a cap. The stomp brings you to the ground very quickly, but its value is in when you use it on a slope to rocket yourself forwards instead of simply sliding mario-style.

Also of note is that Dustforce has other mechanics to encourage speed too. A simple combo system makes sure you're moving at an average speed often, and when looking at the leaderboards you can see how others achieved their best times, so you can see that those speeds are actually achievable.

Point is, for a game to feel fast, at least for me, it requires some degree of effort to attain that speed and some loss of control when you reach it. But the level design must accomodate this and other mechanics supplement it. JJ1 has the loss of control down, but you don't even need to hold down a run button to get to that speed. JJ2, though, is too controllable at its high speed, and you can never move past it.

The game still feels as though it's at odds with itself. Combat in single-player is often boring and easy, unless you have a clever level designer. Jazz can attack from a distance while the majority of enemies can't, so you are essentially encouraged to stop at a distance and take them out before heading through. And you're never rewarded for being fast in any way.

So with all that said, I don't really know how to make something that really feels fast within JJ2. I feel like you'd need some significant AS stuff for extra mechanics, or at the very least some clever level design to make things work.