What if people simply get a "chaser boost" if they are sprinting after an enemy who is sprinting away from them, based on line of sight? This would allow people to catch up to someone who was sprinting away from a bad position, but if they were right next to cover, they could use the cover to break line of sight to the chaser, rewarding good positioning by denying someone getting a speed boost.
Resetting spring when getting shot is perhaps the most unfun thing I can imagine to play. Turf Takover alone is a 12v12 where you almost always will get shot by someone, especially when contesting the objective, so players would inadvertently get "trapped" on the objective. Worse yet, I would dislike it even more if I played PvE and needed to take cover to regen hp for once, but suddenly that aimbot AI hits me out of nowhere and I die because it resets my sprint. The only people profiting from this is whoever happens to chase as noone who gets their sprint reset will have an enjoyable experience. Less than 50% of the players actually will enjoy this (for each player sprinting away, there is one player shutting down their sprint), and it is less since even AI could reset the sprint, and the AI doesn't even have a concept of "fun" or "no fun".
And then even the one who chases after someone can get their sprint reset, which causes their target to escape yet again and we are back to square one.
I like the sound of stamina bars more as it is at least in the hands of the players to manage this and the ones managing it well (or in luck) will have enough stamina left to run away. However, I can't help but think that this is a lazy approach to this subject, as people with equally optimal stamina management will end up never chasing down the other, which is also the main problem of the whole story. Hence my suggestion above about adding a boost to the one who chases.
To me the inherent problem is that characters feel like they walk super slow. You can't really dodge someone that aims somewhat decently, your only saving graze being jumping around like a maniac or server/input lag on whoever is trying to shoot at you (or being near cover, which is not always a given). If characters simply walked reasonably fast then there would be more opportunities to take down a low hp target before they sprint behind a wall, and sprinting itself would then only be used to cover larger distances (like when running to the objective all the way from the spawn or quickly trying to go through a flanking route). Heck, with faster default movement speed, people may not feel like they need to sprint at all and instead shoot back while trying to walk behind cover, resulting in less "cheap" escapes.
But that's just my opinion on the whole thing.
