The controversial Starbucks proposed for L Street and Broadway has been approved, the city said.The approval comes after months of debate over adding a Starbucks to South Boston. Opponents — including Mayor Martin J. Walsh — said the coffee chain location would be too disruptive to traffic and parking, and was not necessary for a neighborhood that already has a number of coffee shops.But supporters argued Starbucks filled a void in the neighborhood by offering a place to do work and an establishment that will be open late that isn’t a bar.