I think I may have a reasonable explanation as to why Church Street (the north-south lane between Seymour and Richards and Georgia and Robson) was so named in the early years of the city. It seems to me that the name may have been connected to Church Parades.
Church Parades were parades of military and/or quasi-military personnel (e.g., police, firefighters) with the purpose of attending a service of worship together. In Vancouver’s early years, the official church which would likely have been attended by such a group was an Anglican one – most likely Christ Church (Georgia and Burrard).
The lane that was Church Street, it seems to me, would have been an ideal assembly location for church parade participants to get themselves organized prior to marching west up Georgia Street the few blocks to Christ Church.