A variety of countermeasures can be used to keep the app awake in the background, including restarting services and (more controversially) location.

And IMO, including a general/non-precise location of contact is incredibly useful for epidemiological purposes and to assist the manual contact tracing teams. The value far outweighing the hit to privacy.

In any case, Google-Apple are dictating how these apps need to be built and released, so private innovation doesn't seem welcome at this juncture.