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Take my advice with a grain of salt, as I am a customer rather than someone running a product with customer support.
I would say this would only feel justified if the product pricing page already had clear tiers outlined for paid support. Putting a price per hour on customer support otherwise would make me feel like I am just being milked behind closer doors for more money, and non-paying customers are getting shafted. If a paid customer support tier is something you offer, imo it should be clearly outlined on publicly available pages with explicit explanation about the differences between free vs paid customer support. You suggesting it in private communications only would feel suspicious and shady to me as a customer.
However, if the customer themselves suggested to pay you extra for that personal support, that’s a different story.
I'd 100% expect that to be a template from someone who either has no clue and can't investigate, or has 200 other tickets to get to and couldn't be bothered to look into a case that isn't in the FAQ. It also does not say what makes you have this assumption and so it works only as a brick wall to alienate any customer goodwill you may have built up. Please never write this unless it's self evident why it's on the customer's side and you have good reason to think they're just trying to annoy you by reaching out despite that
