The Doctor as God angle doesn't work for me.

Sure the technology that he is allowed to maintain the illusion of command over grants him godlike powers compared to humans but really he is a fun, well resourced and slightly potty uncle.

He relives his joy of discovery from your delighted eyes but he can tuck you away when he is bored with you or replace you when you get bored of him.

Your parents trust you with him but he is a bit of an oddball, he takes you to places your parents would never dream of letting you go near, sometimes to places you aren't sure you want to go to but like a fairground ride it only seems dangerous, you are convinced he knows how to keep you out of real danger.

So it's safe right?

Only he is also not exactly honest so perhaps the safety thing is as much a fib as his age and his relationship with that blue shed with the bunk beds.

But you trust him don't you?

Quixotically perhaps?