The water in a Popsicle isn’t pure water. There’s other shit in water. Hate to break it to you but there’s also other shit in the water in your tap or that they use to make food. It’s not all the most chemically pure water on the planet. Sugar in a high enough concentration is a preservative, doubt they’ve reached that in a Popsicle. If you make like concentrated simple syrup which is 2:1 it sort of is, but I think that’s only shelf stable for a few months. That’s basically liquid sugar at that point though and way more than is in a Popsicle. In lower amounts sugar basically acts as food for bacteria.