Maybe it's because I'm not particularly creative but frankly having just learned "Asylum" I'm asking myself "why?".

Maybe it's because the brief tooltip is lacking:

"Envelopes a designated area ... healing any party members who enter .. Potency 100, Duration 24".

So what use is this when Medica II gives a 200 Potency AoE heal and a 50 Potency AoE regen for 30. Sure, I can toss out an Asylum as well but why would I bother?

What situations would Asylum be better than a Medica (I or II) and/or Regen?