Yes, brain activity should be the measure of life. Without brain activity, the person in question would have no awareness of what is going on around them. Since the brain is dead, there would be no chance that the patient would regain this consciousness. Death should be announced once the brain dies.
Without the brain, we are just a collection of living organisms. Brain activity has long been the determining factor of whether or not a person is alive. Many organs can be kept alive and viable by machines. The brain makes the body a unique person and should be what determines if they are alive.
There are stories about people who are still alive and conscious after science thinks they are dead. There are people who have their feeding tubes turned off that are actually alive and fighting for their lives but unable to communicate. A person should not be declared dead until all signs of live have ceased.
People in long term comas can still show some brain activity, even if they are in a persistent vegetative state, and unlikely to recover. It's also possible for electrical activity in the brain to be so low as to be almost unmeasurable, and there are instance of what appears to be post cardiac death bursts of brain activity. The presence of brain activity may not always correlate with life or any meaningful quality of life.