I provide technical support for a small number of children that enjoy Minecraft. Their play involves many MODs from the Minecraft store, frequent adjustment of server settings, and creating new worlds (a new one every 10 minutes).
I have investigated a few Minecraft servers (mostly reading their manuals, I have only fully setup one), but they all appear focused on running a single stable world for a long period of time.
Are there any Minecraft servers that allow the “local” experience?
True, but you’re also basically trying to tell OP to convince a bunch of children that. If they were able to I don’t think they’d even ask this question.