Dedicated servers are an important aspect of gaming. I'll start off by admitting I have a bias - I run a game server provider (GSP), and naturally, we sell a lot of shared game servers ("dedicated game servers") and physical machines to gaming communities, networks, and servers.
Not only do dedicated servers benefit the gaming communities that host them with more control over administration, optimization, mods/plugins, and other addons, but they also offer more choices. Most game developers have limited choices when it comes to server locations - they might use a service like Amazon's AWS or Microsoft's Azure, but even then, it's limited. By renting from game server providers, you as a customer are given an important choice - firstly, who you want to work with. Secondly, who offers the location you want. Thirdly, who you know has good customer support and service.
In addition, community-hosted servers allow gaming communities and clans like eGO to exist. I believe the social groups that play together surrounding games like Team Fortress 2, Minecraft, Day of Defeat, etc are an important aspect of gaming as a whole. Not only because places like eGO are simply fun to hang out in, but also because they do support an actual community feel. They allow gamers to make new friends and play games with each other in larger groups (who even likes 6-player matchmaking anyway?), allowing for more coordination and, in my opinion, fun.
That's not accounting for the game server provider's side of things. Game server providers and dedicated server providers are often, at minimum, a large part of a person's living. Sure - there are many out there that aren't even registered businesses, or don't follow good management practices. But many more are legitimate small businesses to the core, and depend on large-scale games like Battlefield, indie games, Source games, Minecraft, etc. to have dedicated servers. Many game server provider owners take great pride in their work, and are certainly important parts of the gaming community at large that often don't get properly recognized for that work.
Distributors like EA make it hard enough to host Battlefield servers as it is - licenses to host them require thousands of dollars, a complete audit, and the number of providers that can host them is limited. Not giving the opportunity at all is even worse, and frankly, GSPs can be a cost saving measure for the game developer - they don't have to spend the extra cash on infrastructure to support hosting official servers.
That's my two cents, as I have a fairly unique aspect of seeing both sides. Was written quickly, so please excuse any problems
