Electromagnetic potentials are not strictly required for quantization to maintain manifest gauge invariance, as formulations using field strengths or gauge-invariant dynamical variables can achieve the same result.
The claim asserts that electromagnetic potentials are used in quantization specifically to maintain manifest gauge invariance. However, literature shows that quantum electrodynamics can be successfully formulated in a manifestly gauge-invariant manner using electric and magnetic field strengths rather than potentials (Paper [4]), or by building theories directly out of gauge-invariant dynamical variables (Paper [0]). Since manifest gauge invariance can be achieved without potentials, the claim that potentials are used for this purpose is refuted.