For someone with such a successful career, it is rather disappointing that his vision never involved presenting children with a more balanced account of the world beyond what his optimism allowed. It is fine to make a few reassuring tales of personal triumph and inner strength, but there's more to the world than that! Being the standard-bearer of anime, it would not have gone amiss to reveal something less rosy about humanity to his younger viewers, beyond overcooked gestures about war and the environment. Good people can have their demons! Things sometimes don't go our way! Surely the means existed for him to express matters like this.
Do you mean films that are basically wholly depressing or ones that just touch on negative possibilities? I'd say the latter does apply to a fair few of the films that Miyazaki directed. Several of the films involve the need for the characters to grow and sometimes make sacrifices, which means the characters often at least start flawed and that their world isn't the same by the end of the film.
Kiki's Delivery Service, for example, includes a scene where Kiki encounters another girl who isn't entirely pleasant to her. Kiki gets excited for what she expects will be something nice but the other girl is simply not interested. The other girl isn't punished for her behaviour, it's just another life lesson that Kiki learns. There's also the later issue of Kiki potentially losing touch with a friend and her general struggles with trying to run a business. It's maybe not the most in-depth or grim portrayal, and Kiki does get a good deal of support from others, but it does at least touch on more "real" issues.
In Spirited Away, Chihiro's path isn't exactly an easy one either. She's really only able to survive by being mature and rational, she's unable to use the fact that she's a child to her advantage and instead has to rely on herself.
In fairness, these sorts of things aren't necessarily explicit in the films, so it's possible that children wouldn't necessarily pick up on those kinds of details/ideas. Still, I think it's selling the films a little short to suggest they're only a combination of optimism and blatant messages about war and the environment.
On the point about Miyazaki and Ghibli, my favourite Ghibli films are Only Yesterday and Whisper of the Heart. I guess Miyazaki was involved in both (perhaps moreso with Whisper of the Heart) but I don't tend to think of Ghibli as being just about Miyazaki films.
I think it might be interesting if Ghibli was to re-organise and create something new, maybe start a new wave of films with some newer talent. I wonder if they'd consider trying to do something along the lines of what Wings of Honneamise/Royal Space Force did and have a bunch of relatively new talent work on a film that's willing to take a chance on being different.