Sure there are services like BlueNile etc but they're nothing like a Warby Parker for Diamonds.
Diamonds are bought, not because of what they are but what they represent.
The whole point of diamonds is to capitalise on what they're representing rather than their actual worth.
Their value is created through the likes of "diamonds are a girl's best friend" which is why the price is high for them. Hence the advertisements have been developed around the whole perceived value of diamonds ala. "diamond's are a girls best friend" because when you present a woman with a diamond you're presenting her with a promise - a promise that you will look after & take care of her. Which is something that most women want.