I don't know Florence, but compact settlements aren't necessarily claustrophobic or cramped. They can and do have green space and open areas. The difference is that this space is public, not private.

I live in the densest part of a little English town. We have hardly any garden; our house is three storeys high, narrow and terraced. But it isn't claustrophobic. We can go to the town park/playing field, or the water meadow in the valley, or the walk through the grounds of the big house, or half a dozen other places. Yet the town is still compact and walkable, because this open space is shared between everyone, not walled off.