I grew up watching New Who. I never got into Classic Who. Part of it is just that you love the characters and eventually learn to accept that the universe is big and wacky shit happens. The Doctor usually has an idea of whats going on, and that's all you really need. Imo the audience is like an auxiliary companion; we're along for the ride and learning wtf is going on just like whoever's with the Doctor. Our minds can't always comprehend what's going on, but thats okay. We'll figure out a way through and sometimes even save the day ourselves. And at the end of it all we might be a little closer to the Doctor than a normal person, and we can use that to save the world when the Doctor is off saving another one.

ETA: Also the Doctor is a wonderful character. I love everything except the Chibnall era because no one there understood the Doctor. I really really wish we had someone else as the first female doctor because I think it could've been great but instead we got someone who gave more ammunition to the sexists. The Doctor's character has so much depth and mystery and demonstrates an ideal of humanity in the same way Star Trek does. I think one of the best examples of this is in the 50th anniversary special with the Doctor's monologue at the end with the two boxes. I'm paraphrasing, but, "at the end of the day all wars end with what people should've done from the beginning: talk. If people just sat down and talked it out all could be resolved without a single drop of blood. The war you fight will only invite someone to fight another war against you." I'm horribly butchering it but it's a really beautiful speech. It's not a perfect response to all injustice but nothing ever will be. Eventually we just have to stop and move forward if we ever want to see a brighter future.

https://www.youtube.com/watch?v=uCYobBjA1kk