There are so many variables that go into the construction of a home that the short answer as to whether including universal design features in a home compared to leaving them out is that it does not cost any more.
It's a little like asking if it costs more to get a hamburger at fast food restaurant or a sit-down eatery. The basis of the meal is the same - the hamburger and the trimmings - but the presentation, the experience, the expectations, and more set the two price points apart.
In building a custom home, the same thing happens which is one of the fallacies with using the square foot pricing method as a sales tool where the customer is told that the home is so many dollars a square foot. This provides a nice metric but only if the other homes being considered from other builders use exactly the same materials, brands, and components - no difference or variation. Otherwise, the numbers can't be compared except from a very superficial level.
A builder may include a basic front door or one substantially upgraded. The windows - while covering the same opening and letting in the same amount of light - can vary tremendously based on the materials they are constructed of and the brand. Door hardware, cabinetry, appliances, bath fixtures, flooring, lighting, and other components can vary by grade, style, color, model, finish, and brand - offering essentially the same feature but in many different ways. It's a matter of degree.
So, in terms of universal design features, a builder or contractor can design the home to incorporate many universal design concepts that are just part of the essential layout. Nothing special or extraordinary is being done. By using wider hallways (42"-45" versus 36"), bigger doorways (at least 36"), lower window sills, electrical outlets in many rooms that are located higher from the floor, and rocker light switches, nothing really has changed from normal construction except sizes and locations. In some cases, this is already being done anyway. Where the increased size costs a little bit more, it can be offset in other areas of the home, if desired, to balance the overall cost.
In other areas of the home such as replacing door handles on hinged doors with lever style (where this isn't already being done), using single lever kitchen faucets (likely already being done anyway), and installing cabinet pulls and handles that accommodate most people's hands and fingers (easily done), not much of a difference (if any) is going to be required from what already is being done.
There are many other features that fall under the heading of universal design, but not all of them need to be included in every home. Even though they generally are desirable, features such as elevators, skylights, or backup generators may be beyond the scope or budget of your client's wishes - and there are many price points in these items as well depending on size, style, and brand.
Building with universal design is just good design. It doesn't have to cost more to include basic universal design features than building a home without focusing on them, and in so may cases items like light switches and faucets are already universal design. In fact, customers would notice if they weren't included.