What white-glove customer service actually means
Four things, consistently: judgement, context, tone and ownership. Judgement to know when a policy should bend. Context so the customer never has to repeat themselves. Tone that sounds like the brand rather than a script. And ownership, so one person sees a conversation through to a proper resolution.
Response time still matters, but it is a baseline, not the definition. A quick reply that misunderstands the question is worse than a considered one an hour later.