Welcome to permies Svein
Over here it's generally quite valued for floral arrangements and as an insectory plant; I've definitely never seen it take over!
My thinking with compost is that very limited ingredients grown in one place will make compost with very limited nutritional properties.
But I'd most definitely encourage you to follow through on your idea, as there'll be plenty of benefits from the organic matter/waterholding/mulching etc.
If you have access to a variety of ingredients, I think that would probably really help your compost.
I'd also suggest maybe just cutting the plant and leaving it on the ground as mulch in some areas?
I'm not familiar with its habits, but I get the impression it's not that invasive.
Any cows you can borrow?
I forgot to ask where you're from, as that often makes a big difference.