Haskell's type system would not easily prevent this bug. It's not good at numeric/logic issues like that. When people say "Haskell makes it impossible to write bugs" they mean "Haskell has enums" (ADTs).
The big problem preventing this approach from working for numbers is that it's just so cumbersome there. Most of this is because all the arithmetic operators are bundled into a single Num typeclass, and `fromInteger :: Num a => Integer -> a` has a type that's impossible for a "non-zero number" wrapper to satisfy.
make :: forall symbol -> (IsNonEmptySymbol symbol) => NonEmptyText
type family IsNonEmptySymbol symbol :: Constraint where
IsNonEmptySymbol "" = Unsatisfiable (Text "Expected a non-empty string")
IsNonEmptySymbol _ = (()::Constraint) -- empty constraint is always satisfied