This idea is really a copy of enhancement request NIM085436:
Currently Web Maps refer hosted feature services through static rest requests in the JSON. When a hosted feature service is republished with more layers or layers in a different order, the web maps does not update to reflect the changes. This results in the web maps referring to incorrect layers when a hosted feature service is overwritten if the layers have shifted. For an example, please refer to the video in the data path. Please create functionality to have the webmaps update as the hosted feature service is overwritten. This behavior also exists with regular map services being brought into AGOL and Portal via REST URL
In addition, it would be nice if the layer in the web map had an option to set, like "get new layers automatically from service" or something like that, so you could choose which web maps should stay as they are, even when the underlying layers are updated, and which maps should automatically reflect changes in the underlying layers. And/or a button to press to update layers from the underlying services.
Perhaps also an option to choose whether symobology should be replaced with the symobology from the map service when an updated to the underlying service is detected. Or that it automatically detects wheter you have customized the symbology or not. Popups should not be affected on layers where they have been configured when an automatic update is performed.
A workaround for now is to use AGO Assistant and manually add the layer in the web maps JSON-data, but this is cumbersome for most people. You could probably also remove the feature service and then add it again to the map, but this requires reconfiguring symobology (maybe) and popups.
Quick Update: I've written a short guide to update the layers in the web map's JSON data. Please be careful and make a backup. I do not take responsibility for corrupted or destroyed web maps, neither does anyone else. Guide is attached.