Yes, I think that’s a great idea. I’ve added it to my todo list. My initial thoughts are that I will have a dedicated Integrate menu in the top right for managing all integrations (including Beaver Builder, which is currently in the View menu).
For caching, it would be nice to show a little notification icon/number when MT changes have been made but the cache has not been purged (like WordPress shows a number on e.g. the Plugins menu item when there are plugins that need updating). This would hopefully serve to remind users to clear the cache when they have finished making style changes in MT. The first iteration of this feature might just have a button in the Integrate menu though.