I've never understood why there is a long delay between pressing the button on a plain ped crossing and the lights changing.
Any holdoff to prevent multiple re-triggering could equally be applied *after* the triggering, not before.
It causes peds to cross opportunistically before the lights change, thus making the actual vehicle red-light nothing more than an un-necessary inconvenience.
It may be poor programming where it's easier to have a certain time from button press to red light, as that doesn't delay the motorists, which is all that counts.
It may be to deal with the mythical youths who hover around the button and press it just as a car is getting to where the driver would have to brake quite hard.
The default setting is probably near the legal maximum time, and no thought at all has been put into programming. Always favour cock-up over conspiracy.
In pre-rush hour Coventry, it's rare to be able to see a pedestrian when driving and stopped at a pedestrian crossing. The delay is so big that whoever pushed the button is out of sight.
I've heard the Mythical Youth argument before, and consider it baseless.
A driver approaching a set of lights is faced with the same situation regardless of what triggers those lights to change.
He has the same responsibility to prepare to stop if they change, regardless of what event triggered that change.
Be it a robot timer, a ped who pressed the button 90 seconds ago, or a ped who pressed it now.
Indeed, most drivers would not even consider what the trigger criteria were. All they see are the green light and vaguely consider the possibility they might change.
The timing from green through amber to red has not changed.
The need for emergency braking has not changed.
The mythical youth could make the need for harsh braking much more common. Without malice on the part of the pedestrian, the pedestrian will press the button as soon as they arrive. That is independent of the arrival of the car, so the time when the light goes to amber is also independent of the arrival of the car. The light could turn amber when the car is so close that stopping isn't possible (including when it has passed the crossing), when harsh braking is needed, or when there is plenty of time to brake. All are possible, and harsh braking is rarely needed.
If the lights to amber change as soon as the button is pressed, the mythical youth could observe the car and wait for it to get to the point where harsh braking is required, and then press the button, making harsh braking a near-certainty. Add 20 s delay and that is very difficult. Obviously this would be an excuse, just like putting anti-bike barriers on bike lanes to stop mopeds.
I've not seen this mythical behaviour, but on crossings with no lights I've seen odd behavior. I was driving in town on a summer evening, so good visibility and little traffic. I saw someone waiting to cross a zebra crossing, about half a mile away as I was approaching, driving at 30 mph. He waited the whole minute it took me to arrive, and come to a halt, before starting to cross. Although he was an old man, who walked quite slowly across the zebra crossing, it took him much less time than I had taken to arrive. I assume that he had seen me about when I had seen him, as I assume he would have crossed if there were no cars at all. It's easy to see that sort of event as an excuse to prevent pedestrians slowing cars.
(OTOH Canada is really strange for drivers' reactions to pedestrians. Drivers seem to stop when you are just thinking about crossing the road, anywhere not just at crossings. As a tourist and not in a hurry, I had vehicles just about emergency stopped when I turned to the road to see if it was clear to cross. With little traffic, I was happy to wait for a gap, and it was expecting to go after the vehicles, but the drivers just stopped)