This relates to the ticked: https://toolset.com/forums/topic/woocommerce-checkout-page-and-shipping-address/ which was closed automatically, but I was not able to replay earlier.
My answers:
1. I have one Shipping Zone set up.
2. I have only single option checked in Shipping Options > Shipping destination: Default to customer shipping address (but I tried other options too).
3. I have Enable guest checkout option, so guest users may proceed with the order. But I tested this option on and off and there were no differences on the checkout page (in terms of shipping).
4. Changing theme to WordPress default didn't make any difference.
Ok, I know the problem. The product has been set to Virtual so I couldn't see the option for shipping. BUT this is to be a service, that requires the address not necessarily the same as billing one, this is why I was sure I'd see the same option to ship a service to a different address from billing. I think I should just stop using "virtual" option for the services (which I used after WooCommerce documentation).