Impact of not updating default AAM when changing from http to https

Usually when you first setup the SharePoint web app you do not have the SSL certificate. So, you setup the SharePoint web app using http:/foo.com

Later on you get the SSL, and update the bindings in IIS for the web application and add https:/foo.com

You then add https://foo.com to the AAM for the SharePoint web application.

Question:

1. What AAM level should you put the URL for HTTP and HTTPS? The default level already has http://foo.com.


2. Should you update the URL in the search content source from http://foo.com to https://foo.com .