Why the fuck does anyone watch the show? Hell, how is it even still on the air? Dude apparently has at least two god-tier items of Plot Device-itude that can do literally anything, not to mention he's immortal and a time traveler. There is no potential for drama unless the characters suffer ridiculous amounts of amnesia and forget all the crap they could do to solve any problem.
The problems he solves tend to either be problems that cannot be solved by technology, for example mysteries, or that are far beyond his Tardis and Sonic Screwdriver.
For example he faced off against beings who only exist when they are not being observed who have the ability to send you back in time using essentially super speed (Weeping Angels). He couldn't just smash a statue or aim his sonic screwdriver at them. He actually had to think of a solution.
Think of it like Dragon Ball Z. Goku can destroy planets and could eat nuclear explosions. Yet that show works because the enemies he faces are just as powerful or even more so.
Superman works even though his enemies tend to be weaker then him because of his aversion to kill. He had to hold back so he doesn't accidently kill anyone.
It works because the show is structured for the Tardis and Sonic Screwdriver.
The Lightsaber could easily be an overpowered weapon in a setting where people fight in Arenas in full suits of armor and metal weapons.