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Not for public routing (others payments through your node), but ONLY for you own payments.

Routing = take others payments and pass them through your channels and forward them to other nodes.
A private channel cannot do that. Not automatically, maybe manually but is a pain in the ass to construct the payment route in CLI. Is the end of the edge.

Here is an example of including the route hints using a private channel

That way I can receive from any other node into a private channel.
Forget about routing with private channels.
Long time ago was a proposal by Anton (SBW dev) making private routing. But was abandoned.