Wouldn't compassion meditation also relax the mind because of this?
If you could meditate about walking to the gallows after being unjustly convicted and do so spreading a heart full of love, compassion, rejoicing and equanimity limitless in all directions, then your metta meditation is rock solid and well developed.
That would be the painful practice with swift insight discussed in AN4.163:
And what’s the painful practice with swift insight?
It’s when a mendicant meditates observing the ugliness of the body, perceives the repulsiveness of food, perceives dissatisfaction with the whole world, observes the impermanence of all conditions,
and has well established the perception of their own death.
You might prefer instead the pleasant practice with swift insight meditating on the breath:
And what’s the pleasant practice with swift insight?
It’s when a mendicant … enters and remains in the first absorption … second absorption … third absorption … fourth absorption …
Both are effective.