Why would absolute rulers approve of or support machiavelli’s ideas on being feared rather than loved?

He says love is internally based. It's a feeling you largely choose to feel, that you can large turn on and off easily. Love is fickle. It comes, it goes.

Fear is much more predictable and largely externally based. Lovers can fall out easily on a fast downward spiral whim; fear does not wear off if your base character stays the same.

But note the "if you can not be both." The highest way is to be held in love, esteem, and respect during daily life, with something in the back of a person's mind that if they do wrong by you, you'll be a source of hell and misery. That keeps wanton destruction and arbitrary betrayals in check.

I think love is stronger than fear. A commander loved by his soldiers will defeat a commander feared by his soldiers in almost all battles... but the feared commander is less subject to arbitrary chance. So, they both have value. 95% love, 5% fear is probably the best mix. But the 5% needs to be you unleashing the forces of hell with cold precision if you're turned against.