The first cut is the.... most productive?

It certainly does lose a lot of bulk quickly. The morning after layering it up in a dalek with cardboard, it had already sunk a foot.
It's such a nice change to have so much material for the composter, compared to how I've been scrounging around before.
I'll use it as mulch directly as you suggested. Grass cuttings are all new to me, as I didn't have a lawn before