Rented storage comes at 1

per 10 barrels and day, so a warehouse will be more cost-efficient if it is used to a certain capacity. The reason why some players avoid them can be found somewhere else: they require building space and construction workers' time, which can be invested more efficiently into production plants or houses. If you do not intend to max out your cities, go ahead and build some warehouses.
I remember doing some calculations about the tavern mission and I found that it was worth accepting if you can provide for more than 5/7 of the required storage yourself. However, I considered the warehouses "free" as they were there anyway. If you build them specifically for the tavern mission, figures will change dramatically.