The grace period is already fine. A red light means do not enter the intersection. (If you are already in the intersection, then yes, you should get out as quickly as reasonably possible.) A red light camera should only be triggered when a vehicle crosses the stop line after the light has turned red - that is the definition of "running a red light."
The amber light is a signal that the light will soon be changing to red. When the light goes amber you are supposed to stop if reasonably possible. If it is not reasonably possible to stop before the intersection then you should have no problem passing the stop line before the light goes red. The amber light should last sufficiently long to allow that.
The main failure point with this system is too many people treating the amber light as a signal to speed up to avoid the red light - and many people doing so when it's far too late. The main problem with the red light cameras is when they are used as an income source rather than a safety device. Some places have found they can increase the income from the cameras by shortening the length of the amber light. Doing so also likely increases the risk of accidents caused by people making emergency stops because the light just went amber and they don't want to get a ticket. So the desire for increased income can change a "safety device" to something that increases the risk of accidents.