@Erbswurst
In a forest, that works. In a small garden compost heap, the reality is that all those twigs end up making it a nightmare to empty and use the soil around the garden.
It has to be appropriate to your garden.
That means soft stems are fine, hollow ones are excellent, but woody ones get stripped of their leaves and soft tips. If you can shred or really crush the rest, then excellent, if you can't then don't clog up your smallish compost heap or bin with them.
Either stash somewhere where they can rot down slow, slow, slow....beside other slow rot stuff like turfs perhaps, they take about as long to break down, or use the organics recycle bin. The council will shred them and they'll still end up as soil.
Birch twigs (full of the same stuff that the bark is), beech, rowan, willow, wild cherry, pine, leylandii, holly, sycamore, hazel, wych elm, ash, oak, alder, elder....these are all windfalls in my garden, they do not rot down quickly in a compost heap. They do form twiggy snarls that are a pain to get out of the heap or bins. They don't dig into the flower or vegetable beds well either, even half rotted. They end up forked out time after time and returned to the base of the next compost bin in use.
I really don't find them worth the effort. In the woodland along side my garden though, their slow decay is excellent for making the soil of the understorey mixed with the annual leaf fall. But it's slow, and most of us work by the year in our gardens, not by the decade, when making compost.
In my garden, like many others in the UK, open compost heaps don't work well. They just sit and moulder, they don't heat up and they get water logged and they freeze in winter. They need a good cover of some kind.
I don't want the birds rooting through them because they leave it an unholy mess over the path beside the bins, as do the badger and the fox when they raid it for worms, and I really don't want to encourage vermin in to feast on fruit and veg remains.
I've lived here for over thirty years, I do garden organically, I don't use weedkillers, I hand pull every one, but the reality for most of us is small gardens.
These days I use the black dalek shaped compost bins. They're easy, they're effective, they sit under the wild cherries and the lilac beside the greenhouse.
They don't stink, they don't get soaked and they don't freeze, and I get absolutely brilliant worm worked soil from them
I'm happy to see the robins, wrens, blackbirds and bluetits down to feast when we're opening one of the daleks up to empty it
I think every garden is different, and no one system will work for everybody in their situation. In the UK though, if you're not making a massive compost system, hap it up. Cover it with something, keep any warmth and moisture in the heap and try to keep the vermin and flies out.