Using UML is like looking at your feet as you walk. It's making conscious and explicit something that you can usually do unconsciously. Beginners need to think carefully about what they're doing, but a professional programmer already knows what they're doing. Most of the time, writing the code itself is quicker and more effective than writing about the code, because their programming intuition is tuned to the task.
It's not just about what you're doing though. What about the new hire who comes in six months from now and needs to come up to speed on the code? What about five years from now when everyone currently working on the project is gone?
It's incredibly helpful to have some basic up to date documentation available for anyone who joins the project later. I don't advocate full blown UML diagrams with method names and parameters (WAY too difficult to maintain), but I do think that a basic diagram of the components in the system with their relationships and basic behavior is invaluable. Unless the design of the system changes drastically, this information shouldn't change a lot even as the implementation is tweaked.
I've found that the key to documentation is moderation. No one is going to read 50 pages of full blown UML diagrams with design documentation without falling asleep a few pages in. On the other hand, most people would love to get 5-10 pages of simple class diagrams with some basic descriptions of how the system is put together.
The other case where I've found UML to be useful is for when a senior developer is responsible for designing a component but then hands the design to a junior developer to implement.