Are two coats of primer needed.?

Over the years I have noticed that often there is a recommendation for two coats of primer. If the purpose of a primer is to create a bonding layer so that the paint will adhere properly than why two unless the previous color shows too much? I’m changing a brown colored lacquer finished vanity to a white color. After a coat of BIN I intend to apply two coats of the final color. (All sprayed) The primer has hidden the brown completely so would there be any benefit to a 2nd coat of primer?

When I go for 2 coats of primer it is for grain filling and leveling, generally on bare wood.

While the "primary" job of the primer is adhesion, I find that the overall quality of the finish improves when the first coat of primer is applied, allowed to properly dry and is then lightly sanded smooth before the second coat of primer is applied. This takes care of any nibs and other roughness that might happen when that first coat hits the bare wood. The better the surface that your top coats will go over, the better the overall finishing result will be.