Interesting. The only place I’ve ever had scooped custard was at Zwahlen’s (and they had what looked like soft serve machines in back and I assumed they had put soft custard in a container in the freezer while they cleaned the machines). According to the USDA, the distinction between ice cream and custard is egg yolks – rather than whether it’s hard or soft.
Most soft serve (like DQ) seems to have lots of air and sugar, lower butterfat content and certainly no evidence of eggs in the recipe.
The first time I ever had Frozen Custard (years ago) was at the late, lamented Downingtown Farmers’ Market and it was soft but definitely egg custardy.