Yes, that stem is necessary... at least for good storage. Onions need some time to dry and cure. Leaving that stem on helps control the cure. A good cure helps with good storage. If you cut the neck too close, it can cure improperly and lead to rotting faster.

Some gardeners will cure without topping at all and braid onions after the cure. I don't' see it a lot, but sometimes.

Yes, commercial growers leave the stem on. Usually it's windrow, topping, then curing before processing. Often onions are field dried, especially in fine dry areas so long as it don't get too hot. Some areas or farmers may use indoor racks or forced air curing if they need to.

Thank you. That's what I was thinking, but it's good to get informed confirmation. The issue is whether onions can cure WITHOUT the stem left on. I was figuring that if you just slice the stem off immediately after harvest, the moist onion fruit would be immediately exposed to the air, which probably isn't smart.

By "topping", I presume you mean leaving the stem on, but cutting it to a more convenient length. No question that leaving the stem full length takes up more room during the cure, but that's what I usually do, and then I trim it AFTER the cure is done and the stem is entirely dry. I either cure with everyone spread out on paper in my shed outdoors, or in my converted garage. The humidity is somewhat lower in the latter. In both cases I have a fan to do good air circulation. Field drying won't work in my situation. Our spring is usually pretty moist.

Yes, topping is cutting the extra off, but leaving that 4-6 inches like you are currently doing. If you sliced off the entire stem immediately after harvesting, the onion would dry uneven, improperly, leaving too much available to rot instead of cure into a nice dry seal.