Sure, and pi is the limit of a sequence of rational numbers, but lots of properties that hold for rational numbers don't hold for pi.

As you approach sphere you lose Rupertness.

Limiting behaviour can be counterintuitive. As you add vertices to a polyhedron, some properties approach those of a sphere (volume, surface area), but others just get further and further away (number of surface discontinuities). It's not at all obvious which way "Rupertness" will go, or even whether it's monotone with respect to vertex addition.

A sphere has no faces so it's not a convex poloyhedron.

Correction: a sphere has infinite faces so it's not an "convex poloyhedron [sic]." A convex polyhedron must have finite faces, so apeirotopes aren't allowed.

A sphere has no faces, not "infinite" faces.

Convex polyhedra are required to be finite polytopes.