The idea: I see that the Amasty Shipping Table Rates module is overriding the shipping.html template. I think it's better to override the shippingMethodListTemplate instead.

How it works: The extension overrides the shippingMethodListTemplate and only adds the rates table. 

Business value: It would be more compatible with different checkouts. I created a plugin for this but maybe it's something you can change in the module.