Yes, well, removing shipping from a distribution (Commerce Kickstart 2) that has it so thoroughly baked into the configuration is a bit like removing certain kinds of needles in a needle stack.
I would guess, and this is only a guess, that there is a rule that handles free shipping that might be interfering with checkout. Somehow your line items are getting removed from the cart the moment you try to view it, which leads me to think the recalculation is breaking down. Best thing to do would be to turn on Rules Debugging mode and see what happens when you try to view your cart.
BUT! It would likely take you less time to rebuild a stock Drupal site into Commerce Kickstart than it would to go through and pick apart the Commerce Kickstart 2 spaghetti bowl:
For the catalog, see this post: https://commerceguys.com/blog/commerce-module-tuesday-commerce-search-api
For the administrative backend, see this post: https://drupalcommerce.org/blog/7854/commerce-module-tuesday-commerce-ba...
Features was used to create Kickstart 2 and with it's interdependencies, there are number of basic commerce things Kickstart 2 just can't do well if you try and remove the functionality (instead of simply hiding the functionality). That is why it's probably better to start over and only enable the modules you need and follow the two above posts for reproducing Kickstart 2 without Kickstart.