> Making them part of the OS and character set so they could be used anywhere and not just on a web forum was what made them the emoji we know today, and what caused them to catch on.
That's not quite right. The Unicode emoji we use today are directly descendant from the emoji that were on Japanese phones.
That's how emoji ended up on our keyboard: Apple added them to the Japanese iPhone keyboard to be compatible with Japanese carriers; users in the west discovered this and started enabling Japanese input on their phones to use them; finally they became so popular that Apple (and Samsung etc.) also enabled them for non-Japanese keyboards.
If not for the original Japanese emoji, chances are that every website would still have their own smileys, instead of there being a single, interoperable set.