The Burn being caused by a magic baby having a tantrum kinda ruined the whole setting for me

The Burn has one of the most classic Star Trek explanations ever—normal human(oid) gains magic powers after being exposed to strange energies. The Burn was several classic Star Trek stories woven together to tell a new tale. It's basically a retelling of the TOS episode Charlie X.

Trauma acting as the trigger for those powers is the most believable part of the Burn. Emotions causing people to react is nothing new. It's how humans operate in real life. Entire wars have been started over the death of a loved one. Emotions acting as a trigger is not new to Star Trek either. It's been used a motivation for dozens of stories.

Star Trek has used the trope dozens of times and several in an almost identical scenario. Such as when Kevin wiped out the Husnock in response to them murdering his wife. Or Riker breaking his promise not to use his Q powers after Wesley was killed. It's a realistic human(oid) response—trauma like the loss of a loved one can trigger a reaction with no bounds.

tantrum

It's really disgusting anyone would refer to the grief and trauma one experiences over the loss of a parent as a "tantrum." Your comment is the very definition of hyperbole.