Is there any point in putting solid stain (rather than paint) on LP Smartside?
differences... between solid stain and paint?

Although there is a huge variety of products and no hard rules for naming them, solid-color stain (in general) is usually used on rough surfaced wood because it is typically thinner and will not hide the texture like paint will. It is also generally easier to apply to rough surfaces because it is thinner.
As to your question about the difference, not much. Solid-color stain is not a penetrating stain as you presume in your question. Like paint, it forms a cured film on the surface, benefits from having a primer applied, and can bubble and peel on improperly prepared surfaces just like paint will.

...is there any reason at all not to just use paint?

Yes, and no. I find that it is easier to apply (and to recoat later) solid-color stain on large exterior textured-wood surfaces. On the other hand solid-color stains are flat (no or very little sheen) and need to be recoated every so often (like every 2-3 years) to stay looking fresh, whereas a paint with a sheen would give more durability and may not need repainting for years and years.