Lightning - Inputs Will only show you a required error if you enter and delete a value WHAT?

My best guess based on research is that this should be fully functional whenever the element goes out of beta, most likely Summer '17, if the prerelease notes are any indication.

the Required highlights and message only appear IF you enter a value then remove the value (interact with the field)

This is how every UI element in Lightning prefers to operate. The idea is to keep as much red off the screen as possible. The Classic UI did this, too; there was only a red bar until you hit a button, then you'd have a red box and error message. Don't worry, your users will probably get used to it, unless... (spoilers ahead)

You can check for validity and it will return null if the user has not interacted with it

Validity in Spring '17 is guaranteed to be returned, according to the release notes. It's working in my Spring '17 sandbox.

I see no way to cause the message to be displayed from the component controller when checking validity

For now, it looks like the correct method is:

    var field1 = component.find("field1input");
    if(field1.get("v.validity").valid) {
        // continue processing
    } else {
        field1.showHelpMessageIfInvalid();
    }

Or, perhaps...

var field1 = component.get("field1");
var field2 = component.get("field2");
// ...
field1.showHelpMessageIfInvalid();
field2.showHelpMessageIfInvalid();
// ...
if(field1.get("v.validity").valid &&
   field2.get("v.validity").valid // && ...
) {
    // continue processing
}

However, it's not in the Release Notes (yet), so I might be jumping the gun. It does (currently) work in Spring '17, but might change before the final release.

If you really wanted to call out a field on init, showHelpMessageIfInvalid would do that, too, assuming we get access to it. Here's hoping.

This is supposedly getting fixed in Spring '17. I can't deep link in the PDF but check page 388 for details on the change. I have not checked this out in a pre-release org yet.

https://resources.docs.salesforce.com/206/latest/en-us/sfdc/pdf/salesforce_spring17_release_notes.pdf