Regen delay is from the controller. Different controllers will have a shorter delay or none. Some that are programmable might have this delay as an option that can be set. Some controllers have variable regen, that can be controlled with a throttle. All programmable controllers that I know can be set to automatically regen on throttle release, that is acting like compression on a gas engine.
In every case, regen is not constant. When the difference between controller voltage settings and battery state of charge is little, regen can’t be powerful, but as the battery voltage gets lower the regen does kick better. Variable regen does give it a better functionality, by giving you control of regen braking, making it better able to replace your brakes. Good brakes are always more precise and efficient than regen though. You will never achieve a shorter braking distance with regen than with good brakes but, both combined together can improve your braking distance in some slippery conditions.