What does ‘On its good days’ of “On its good days, all this (live for love, die for love, kill for love) seems to make perfect sense mean?

Solution 1:

It's nothing to do with the idiomatic greeting "Good day".

When one (of those people who live/die/kill for love) has a good/positive/enjoyable day, they naturally feel their outlook makes sense/is vindicated.

And that happens often, because such people tend to have lots of "good days".

It's also possible it's the article writer to whom live/die/kill for love seems like a sensible life-plan. The words themselves are ambiguous, but I'm swayed to the first interpretation because of the reference to such people having lots of good days.

Since presumably the writer isn't a "love extremist" herself, she wouldn't have the good days. And thus probably wouldn't think in terms of such an outlook [only] making sense on those days.

Solution 2:

The quote does not refer to good day as a greeting, but to the idea that people fare better on some days than others. It's a common expression for people suffering from afflictions; from “Good Day – Bad Day,” an article about coping with cancer:

Coping with a health problem is different for everyone. What is helpful is taking a look at what happens on good days and bad days to work towards having more good days. Doctors, families and friends can use this information to help you.

The Time article refers to love in a similar way, as an affliction that has good days and bad days for the people experiencing it. “On its good days,” love justifies people's belief in it – and the author emphasizes that “love has a lot of [good days].”