This was likely true in your grandmother’s day, but in today’s world there is no standard. Every vendor has a different scale by which they determine the designer’s discount, which can range from a slender 10% to a very healthy 40%. Mostly, this is based on what it costs them to acquire or manufacture the materials or items of merchandise your designer is selecting for you. The costs of labor and raw materials constantly chip away at this.
To your point about why you hire a designer: I would suggest that hiring a designer for the discount they provide is doing you both a disservice. A designer should be engaged based on their design talent and on their ability to help you spend the money you have allotted to your project as wisely and efficiently as possible (this may mean you need to be very realistic about costs…and do less). For most people, this is one of the biggest investments of their lives. Focus on the designer’s ability to minimize the margin for error and maximize your long-term enjoyment, rather than on specific discounts.