There are several reasons to wear doubles. For some, it's to provide gas for longer duration and/or deeper dives. And yes, this can and will result in a decompression obligation, which with proper knowledge is a perfectly acceptable requirement.
Others wear doubles because of the increased safety they provide... two regulators, two valves, two separate gas supplies (assuming an isolation manifold is used). This is the main reason I wear them diving up north. I dive alone frequently, and even when I don't, my buddies tend to follow the "same lake/same day" buddy system. The water is very cold here, so reg freeze-up is always a possibility, so having the ability to shut down one post while maintaining gas is kinda nice. In other situations... wreck penetration, caves, under ice... all demand redundancy to be done safely.
Many of the folks I dive with also carry a third, or even forth tank with various deco gasses to reduce deco time and increase safety as well.
You are in the tech diving forum, and I'd bet the price of an airfill that virtually everyone in here either wears doubles on a regular basis, or aspires too...
Finally, they feel nice on your back. If they're set up properly, they are balanced nicely and a joy to dive. Most folks here that are in doubles, wear steel tanks which help to sink a drysuit and greatly reduce or even eliminate the need for a weightbelt.
Does that help?
Wearing a single tank is a great limiting factor in terms of what a diver is capable of doing. It is also a bit like a governor on a car... within reason, it prevents a diver from getting into too much trouble (although many still manage too). But "extended range" diving requires more than just a set of double tanks. It requires training, practice, a good brain and a willingness to learn from others,