Make sense. I endup with this setup. I'm still wondering if I could run a node with just private channels to (hopefully) good peers and still have an ability to receive payments (for merchants using an account on lnbits connected to that backend).

Privacy aside (for sake of simplicity). I don't need to (or want actually) route. I need the merchants be able to receive. 

 Sure, why not?
I wrote several guides and here you have some that you could run two powerful private nodes on your mobile device:
- https://darthcoin.substack.com/p/getting-started-zeus-mobile
- https://darthcoin.substack.com/p/getting-started-with-blixt-mobile 

 Why not is the question.

Is there a disadvantage in having just private channels? Is it more likely a route to fail for incoming payments with only unannounced channes?

For small payments never. For bigger one (like 0.005) I can't tell if it's because of bad connection or discoverability (if it's a word)