It takes away the JUMP (yeah, the most SACRED thing in shooters) but it substitutes for it with the leash and slide mechanic that is actually more useful than you might think.
Sliding in this game is not just a trick to get to cover quickly, it's an honest to got powermove that sends your enemies flying like a canon ball.
This creates cool combos, such as when you deal with shotgunners who wear thick head armor that completely blocks bullets. One kick sends them flying with the vector of the kick being against their legs, which in turn exposes their head for a kick, which shatters the head armor and extends stasis, which you can immediately follow with a nice clean headshot. And when the game actively assigns points to each and every "skillshot" you find yourself doing that more and more.
I think this can be analogous to DOOM's Glory Kill system: Without it, you'd just crouch behind cover for pop-and-shoot whackamole action, but since enemies drop little ammo, and ammo is purchased with skillpoints, you are actively engouraged to be in the action as much as possible and use kick, leash (which pulls distant enemies towards you) and environment to do as much chaos as possible. I think such a system plays very nicely with regenerating health.
Instead of stop and recover action it becomes a game of how much punishment you can deal without getting hurt yourself, prioritizing enemies on the go and improvizing with environment to the best of your ability. The best way to play despite what your regen-shooter instic will tell you is to just get right in the middle and start kicking ass, both figuratively and quite literally.
Also I really-really like the juvenile sense of humor bulletstorm has. There's a distinct type of skillshot that involves first shooting an enemy in the balls (which triggers a stun animation) and then finishing them off, which is just called "Mercy" and that sounds pretty meh on it's own but it's all over the game.
It's like how Noah Gervais describes the value of the very first sex scene in God of War: While being extremely tacky and kinda sexist in the later games, the first instance was well hidden and almost feels like just a sick prank on developers part. In words of Noah, "If developers were standing next to player in that moment they'd be laughing and giving high fives to each other just for making you sit through the cringe", and I feel like the whole system of skillshots is just that.
And here's the rub, the main villain in the game is this stereotypical drill-instructor type general that hurls obscenities, juvenile jokes and racist slurs all over the place to the point of even the main character, who's fairly obnoxious himself really, really hates the guy. Nobody likes his personality and it just turns out that the whole skillshot system is his idea to reward soldiers who perform well with ammo and leave less skilled to die.
In other games I'd ask for a less toxic, more well thought out villain but in this game the burning desire to just end the motherfucker in part because he's just a cheap villain fuels your entire journey. From the moment he joins your party late in the game and up to the moment where you finally get to throw down with him in an epic QTE cutscene you really, genuienly want to finally shut this fucker up, forever.
Also on the side note, there was one moment when a female character gives you a timed puzzle to solve and promises to grant you a wish if you do, and I was prepared for the absolute tasteless blowjob joke and then protagonist just says "Hey, you're not really dealing well with my friend here, but he's been just recently physically maimed and seen some shit, can you try to be nice?" and I found that really adorable.
In another instance, the aforementioned friend named "Ishi" gets really pissed off that he got into this mess because protagonist was drunk, and says that he will shot you if you touch a bottle when going through a poolside bar, and if you really don't touch a single bottle in that segment he'll commend you on being sober for once when being around the bottle. This was also a nice little moment that offered a glimpse at their relationship.