[previnder]

Well, the problem is that people use the word 'love' to refer to all sorts of things from sexual desire, to attachment, to kindness, compassion, and benevolence.

The Pali word 'mettā' means something quite similar to 'agape'. In Buddhist traditions, mettā (or loving-kindess) meditation is all about cultivating this sort of sentiment by conscious effort. From the very little I've practiced this, I can confirm your point about how benevolence, for some reason, reduces fear and anxiety (often we aren't even aware that it's there).