But that sounds weird... if it is the pursuer declaring a chase. Why would a pursuer want to switch to chase rules, when the "sticky" combat movement rules make it very difficult for someone to flee?A chase begins when someone, player or DM, declares an action to pursue a creature that is moving away. Whatever distance away from the pursuer the fleeing creature is when pursuit begins is the starting distance.
I mean, the foe moves away... you just move back close to it. This is always advantageous to the pursuer because of Opportunity Attacks, whether the quarry tries dash, disengage or dodge. To have a chance the quarry needs a higher base speed, only in that case maybe a pursuer with a higher Constitution might think it has a better chance of catching up in a chase.