Restrict Access Requests to Whole Site Only

[TonyS]

I have a SharePoint site, I believe it's running on Office365, where I have a number of libraries and folders with unique permissions.  I would like to allow new users to request access to the whole site, which will allow me to accept their request by adding them to my default group.

However, more often than not, new users are requesting access to a library with unique permissions. 

This forces me to:

• Manually add them to the default group
• Accept their access request while only giving them restricted read access (because otherwise they don't follow that they now have access and will email directly)
• Then manually remove the new user from the site permissions (as I don't want them being given permission directly)

Is there some way to allow users to only request access to the whole site without allowing them to request access for any library within the site?

[#2]

Adding an update to my initial statement.

When new users are requesting access to one of my libraries, instead of the whole site, the request is somehow coming in as granting them "edit" permissions for that library.

This is the most painstaking part due to the drop down for permissions not allowing me to select a group.  Instead it comes up as "edit" permission by default, and then I have to manually change that to restricted read so they do not gain additional privileges before I can remove their direct access.