Linear time is boring.
The Doctor has tried it before, he grew up in linear time, but he didn’t really like it even then. One day follows another, everything happens in order, effect following cause. It’s all so predictable and… safe. There’s no uncertainty, no adventure, no risk. It’s just sort of blah.
Give him a life out of order anytime, where cause sometimes follows effect and you meet for the first time people who’ve already know you for years. Jumping around in time is exciting, unpredictable, and best of all it means he can skip past all the boring bits. He never knows where he’s going next, sometimes doesn’t even know where he’s just been, but it doesn’t matter. Every day can be a new adventure.
He has a TARDIS and he’s not afraid to use her. He can go anywhere in space or time, watch solar systems being born, meet famous people before they’re famous, see the most momentous historical events as they’re happening, and because he can, he does.
If he’d stuck to living in linear time, he’d still be plodding along, one day to the next, never seeing or experiencing much of anything unless it happened in his own timeline. Where would the fun be in that?
He realised a long time ago that he just wasn’t cut out for linear life, couldn’t bear the thought of everything that was out there passing him by. That wasn’t living, it was merely existing. Let people living everyday lives worry about everyday things like mowing the lawn, washing the car, or walking the dog.
He has a universe to save.