Representation is an existence claim
Under stated conditions, a network can approximate a broad class of functions. The result says that suitable parameters exist, not that training will find them efficiently.
Finite data changes the problem
Real models learn from samples. Generalization depends on the data distribution, inductive bias, optimization and evaluation — none is supplied by approximation capacity alone.
Use the theorem at the right altitude
It is a foundation for thinking about expressiveness, not a certificate for a particular architecture, dataset or deployment.