I agree that the "immediate countdown" pedestrian lights are ridiculous, but I'm used to them.
As for it being illegal to start crossing if the red hand is flashing, I find I'm usually not able to start crossing immediately anyway, either because there is a crowd of people waiting ot cross and we can't all start at once, or none of us can start because there is some minor gridlock.
What does bug me, however, is that at all intersections I use regularly, the lights cycle automatically, but in other neighbourhoods there are some that stay red unless someone pushed the crossing button. Expect to hear cursing from people waiting to cross, and didn't realize it's one of those. If you only realize a moment after the traffic light turns green but the pedestrial light sits there at red, the button may not work and you have to wait another cycle.
Similarly, buttons work differently at different intersections. Some buttons have to be pushed to get the crossing signal when the traffic signal changes, some have to be pushed to force the traffic cycle to start because the intersection stays green in one direction until either someone pushes a button, or detectors determine a car is waiting to cross or turn left, and some say push for audible signal only. Recently I had a woman yell at me because I was waiting to cross, and had not pushed the button. I pointed out the sign that said push for audible signal only, and she kept yelling and insisted those signs don't mean anything, and not pushing the button was delaying the signal change. I was partly annoyed, but also partly sympathetic, because it's understandable that people are confused when crossing buttons can do any one of three different things.
What we need is consistency. Every intersection's crossing button should do the same thing. We shouldn't have to read a paragraph on s sign to find out what the button does.