I never use domes. High humidity and high water content of the soil inhibits root growth. The plants don't get water stressed so they don't grow strong roots. Peat pellets tend to dry out quickly so a cover is useful until the seeds germinate, but then can be removed. The whole peat pellet, dome thing is a marketing gimmick, although your hands stay a little cleaner than when dealing with pots and mix. Unlike peat pellets (many times), small cell flats or plastic pots will retain moisture long enough for most seeds to germinate, then you just have to water them when they start to get dry. The potting mix is usualy more nutritious for the plants as well and you need it for potting up later anyway.
When I do tissue culture techniques, and plants are grown in closed sterile flasks, the way to harden them off once they come out of the flasks is to remove the covering until the plants begin to wilt and then cover them up again, repeat the next day. Once the plants do not wilt they can stay out the whole time. You can also partialy remove the cover a bit more each day, but you don't have a progress indicator the way you do with the wilting.