Don't get me wrong--drying racks don't get a 'dedicated space' in our 1000 sq ft of paradise! They only come out when they have work to do; the rest of the time they are folded and hanging high on the wall!
I don't have room to dry anything flat if it is too big to go on top of the rack.
That 'too wet to hang' problem went away when we got a Miele washer with a spin cycle that really spins much more of the water out than the cheepie washer that came in this condo.
As for putting a wash friendly jersey in the washer in a cold cycle, it should be fine. It is probably good to keep the zipper zipped in the wash so it is only one weapon rather than two. I also go a little overboard with laundry (lingerie) bags for lots of our wool items so that the base layers don't get as beaten up, but it is probably not necessary.