For 3 Blue mana, you get a token of a target creature you control. Also, like all five cards of the Fated cycle, if you cast it on your turn, you scry 2. Mono-Blue Devotion had a fair share of things it would like to copy, including Tidebinder Mage and especially Master of Waves.
A Triple-Blue casting cost is obviously no problem in a mono-Blue deck. Still, it does limit its play-ability to mono-Blue decks for the most part. This definitely seems like a card you wouldn’t cast during your opponent's Main Phase. It always seemed to me to be something good to play at the end of your opponent’s turn.
I've always really liked this card, especially because it’s instant speed. Then, because the token is a copy, you get even more devotion out of it if it's a Blue card. To me, it seemed a solid addition to an already powerful deck... but did anyone actually play it in Standard?
Unfortunately for Fated Infatuation, it never really became a staple in Mono-Blue Devotion. However, some lists did adopt it, like this top Devotion to Blue list at a Last Chance Qualifier for GP Phoenix in 2014. It seems that it was a solid one-of, although it doesn't seem that any other top lists played it.
However, the card does still see some play. Fated Infatuation has also found a few homes in Commander, but most especially in Temmet, Vizier of Naktamun decks. It's a token-happy deck already, which seems odd in White and Blue, but it's a playable deck. Fated Infutation doesn't care if the creature you're copying is a token, either, so it's a solid addition to that deck. Really, any Commander deck that likes to copy things, such as Sakashima the Impostor or Riku of Two Reflections, can make sure of this handy Instant.