(Did you notice that a new routing provider has been included there silently, namely Valhalla by mapzen.com??)
Sure
But I (as a normal user) would recommend to include Graphhopper car routing only to
main osm.org website only as soon as car routing has the feature of turn-restrictions.
Yes, exactly that is the reason it is currently not there.
Is it correct that the latest developemnt about this is in (after browsing
many github issues) Turn Costs for CH · Issue #270 · graphhopper/graphhopper · GitHub ?
Exactly, there is also a first step already here
Maybe we can figure out what technical step has to be done first for this feature?
Contraction Hierarchy needs to work for edge-based graph traversal too, which is not that complex but a huge effort and will take 3-6 weeks.
I once thought about a crowd funding campaign about this, so that potential interested (commercial) users would sponsor only a small fraction and I would not need to take the riscs and costs of this feature. But before we start with this campaign we need to make main parts of flexibility work happen.