I admit, going rates serve one important role in pricing: they signal the average price, and thus set the expectation about the connected level of quality.
Average quality and average price go well together as a message. Offering a lower, bare-bones quality and a price below the going rate is also fine, as is going above for a more specialized service.
But whatever you do, never go “better than average, and cheaper too.” It may sound like an irresistible offer, but when viewed from the client’s eyes, often it’s as irresistible as an “inheritance” left to you via email by a Nigerian prince.
Even if what you say is 100% true and objective, an offer like that makes most people think my dear are you really dumb or do you think I am? What looks too good to be true usually is – not true.
Logically speaking, if someone was truly good at [what you do] they would have a lot of work. If they had that, they would never need to discount. Therefore, if your price is below the market average, you must not be as good as the average!
You being an expert, a “safe pair of hands” is a message. You asking for a price that does not fit what an expert would charge creates another message, inconsistent with the first.
To avoid asking your clients to suspend their disbelief before they even met you, make sure you set the price to represent the quality of service they can expect to get.