Yet again, that's subjective. I've played a lot of the maps without sprinting (it can be risky in SWAT) and it does not feel like a crawl. And those same maps work with sprinting to cover the distance of a hallway, or make it into a doorway while under fire.
You're being over dramatic.
BMS and sprint aren't that far apart in terms of speed. As far as how long it takes to get places, it's down to map design based on the mechanics implemented. Sprint isn't going to get you places faster than intended, clamber isn't going to get you over walls and up places you're not supposed to get up to.
Whatever issues there were with Halo 3's speed / sensation of speed is far easier fixed with other options rather than implementing a game changing mechanic like sprint. I'm fairly certain Halo 5 has a different FoV, different acceleration values, map design ideas, aiming mechanics and whatever else contribute to a sense of going fast, not counting the advanced movement mechanics.
So basically it comes down to the gameplay these advanced movement mechanics offer.