I think that it's not meant to replace those. It's meant to replace the act of passing your phone around in person — say, around a dinner table — in order to show photos to the people you're with.
Now I have to ask everyone to pull out their phones.
"Mine is in my purse, let me go grab it" "I left mine in the car, oops" "My battery is dead"
Then I have to text/email them the link.
"I didn't get the link" "I have no service here"
Whereas, passing a phone literally takes a millisecond.
It's certainly easier to pass around a phone, of course, but I can see the flaws.
This is a place where NFC would really be a step up though. Tap-to-share-screen, instead of having to find contacts and numbers and sending texts.