I wonder if an artificial sweetener like sucralose or erythritol could be used to make a reasonably soft ice cream.
Weeeellll...remember, the sugar in ice cream helps it not form into a solid chunk of ice (as does the fat). Often reduced-sugar recipes call for alcohol, which can help do the same thing. You're really going to need something to keep all those ice crystals from forming.
If you want to play with artificial sweetener, I'd be tempted to suggest going more towards a frozen custard. My first trial for such things would be milk, a sweetener, and cornstarch. Once you have a custard that you're ok with, try running through your ice cream maker. I've tried something similar, but I didn't have an ice cream maker at the time. I ended up with something like a pudding pop. It was still yummy.
Erythritol (or a comparable compound) is a sugar alcohol that will have some of the physical properties of an actual sugar, and will be a bulk ingredient. It will likely have a textural impact on an ice cream compared to there being no sugar at all, which might or might not be desirable.
Sucralose is a 600x strength artifical sweetener that you would, in its pure form, usually only add in far too small quantities to have any textural impact, so you would get the same result as making the ice cream with no sugar.