Well obviously we just need to make them Fire/Police/Bike Lanes and size them appropriately!

Where the cyclists are making their mistake here is ignoring that gigantic opportunity for generously sized lanes and a strong lobbying team. The cops and firefighters already know the cars can't/won't get out of their way, and bikes would be much easier to pull over. Especially because if you were on your bike and heard a siren you would be certain that vehicle is going to be coming down your lane.

I haven't thought this through, but maybe the Emergency Lane should run down the center, bright red and wide enough for two fire trucks to pass each other in case they're going in opposite directions. Then the cars could have their traffic jams and parking etc. in what's left. If the bike lane was a narrow white strip in the center of the Emergency Lane, you might be protected enough by the extra width and red paint that you wouldn't need much physical barrier, so pulling out to the curb in the middle of a block wouldn't be hard as long as you made sure the cars saw you cutting through their lanes. And you could pass each other by momentarily veering into the red.

"This city needs Emergency Lanes with no cars allowed, for our brave Firefighters and Police Officers to save lives!" "But a lot of the time the Emergency Lane will be empty!" yell the car people. "Not if we put the bike lane inside it! Get the spandex squad out of your lanes, and let them be the ones who have to skedaddle, while you drive peacefully along playing games on your phone."

Psychology.