Time Lord technology allows the Doctor to do things nobody else would even consider attempting; it gives him the kind of skills that amaze and mystify others. People look at him like he’s a magician or miracle worker.
Doesn’t hurt his image.
He’s particularly proud of his glass of water in the pocket trick; it isn’t just the TARDIS that’s bigger on the inside. Anyone else would carry liquids around in bottles, but then you have to open the cap to take a drink… His way is more convenient as well as being impressive.
Unfortunately, it can have unintended consequences…