Slips can be produced from the stored sweet potato which survives the winter in storage. I suspect that was one of the major considerations in parts of the world where there's a winter.
If it where a more disease or pest prone plant I would also suggest that it's a way break the cycle of pests and disease that live on the leaves. Maybe it's even why they have such a good reputation for having few disease or pest issues.
If you have a healthy plant to produce cuttings, I have heard good things about people growing sweet potatoes from the plant cuttings. These people grow whole fields this way https://www.youtube.com/watch?v=j4Ntf4Xo-Mg
I've done my sweetpotatoes both ways and it seems that some years the slips direct off the potatoes work well and other years I'm clipping up vine cuttings. I try to take cuttings of each variety in the late summer/early fall and pot them up to bring through the winter....they make attractive hanging basket plants. Don't wait till you harvest the potatoes since it will be cooler and the cuttings will be slower to root. On sweetpotatoes there are some diseases that carry on the roots, and are therefore able to be spread onto the root slips, whereas vine cuttings taken only from the above-ground parts of the plants don't carry these and can break the cycle. But some years my vine pieces just don't want to root, and then I use slips. Usually I plant the smallest potatoes in a pot of flat and let the shoots grow up that way, and then pull them off batch after batch and plant....
Now, I don't bother planting them because they come up volunteer all over. I'm finally managed to get rid of them in a couple of areas where they kept coming back year after year but I didn't want them any more. They send runners under the soil that pop up next year as new plants. Once established, they are hard to get rid of. We don't have a freeze, so they grow 12 months of the year.
I've found that the easiest way to start new sweet potatoes is to go out to the sweet potato patch (in my case, on a hillside under my figs and avocados) and just hack away at the vines. I use a set of hedge trimmers. Then I take the 1 to 2 foot long pieces of vine and toss them into a 5 gallon bucket. I fill the bucket with 6 inches of water, set in on the shady side of the house, and leave it for a week or so. All those vine cuttings quickly spring roots and I have all the slips I'll ever need. I give them away to people who want to start SP's in their own garden.
I mulch my soil heavily with wood chips at least once or twice a year. I generally just bury the sweet potato vines because there are so many of them back on the hillside. They just keep pressing up through the chips and growing. What is beautiful is that the soil under those vines is amazing. Black and crumbly and beautiful. The sweet potatoes help convert all that wood chip biomass into dark crumbly soil. The sweet potatoes that do not get eaten by me (probably 90% of them go unused) get eaten by various soil biota. We get those green fig beetles, and I think that their big fat white grubs are under the soil in the wood chips, feasting on the sweet potatoes. There are more than enough to go around.
"The rule of no realm is mine. But all worthy things that are in peril as the world now stands, these are my care. And for my part, I shall not wholly fail in my task if anything that passes through this night can still grow fairer or bear fruit and flower again in days to come. For I too am a steward. Did you not know?" Gandolf
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