I changed the frontend templates (override by copying the file(s) into my custom theme folder) of the cart and checkout page by replacing some table-row-columns-constructs with div containers in order to create a (in my opinion) clearer layout, also for handling responsive layout changes.
It seems, the Wordpress hook/action woocommerce_checkout_order_review triggered from the template checkout/form-checkout.php template uses the code from cart/cart-shipping.php which is fine, because ist keeps the list containing the choosable shipping methods consistant on both pages.
A 'critical' change was: removing the td and th tags, and replacing <tr class="shipping"> with <div class="shipping"> in cart/cart-shipping.php.
This leads to the problem:
Clicking a list item of the shipping_methods ul triggers the events update_checkout and updated_checkout, which (i think) are responsible for updating the cart/chekout page.
With my changed HTML templates things are not working as they should; with every click the whole ul gets replicated.
I could not find any occurences of tr.shipping or .shipping in the woocommerce js code.
Why is changing the template structure breaking the jQuery code? And how can I achieve that change without breaking?