The low cost is the primary benefit, but there is also the virtue of steaming compost over bagged, soggy stuff that is shipped hundreds of miles or more. Local composting also encourages municipalities to pick up leaves and grass clippings and provides a location for people and landscapers to drop off small tree trimmings, drop, and brush. And late to the game but ever increasing, is a supply of compostable food scraps supplied by food purveyors and municipalities.
My criticism of local compost is that it is often too woody, given how much of it is made from shredded or chipped local brush and tree trimmings. Another complaint I have about compost brought in, meaning not made by ourselves, is that I consider it inactive. When I compost at home, the pile is teaming with visible and invisible organisms. This activity is what provides the compost its boost when given to the garden. Bagged compost is often a cold, soggy mess that needs to be re-inhabited by organisms already present in your garden. The local pile, steaming and faintly scented of ammonia, doesn't have the larger organisms of my home pile. It is, in other words, a less complex ecosystem.
So, every compost has its virtues and those virtues are context sensitive. If you live in an urban environment, bagged compost may be the way to go. In the sub or ex urbs, local compost can be trucked in by the yard and is the most cost effective especially if you extract the delivery charge (usually around $75). Whether in the city, burbs, or country, you can often find a nursery that makes an artisanal batch, bagged and at a fairly high price.
All told, the best compost is extremely local, it is your own. Now, I've got to get that new pile started.