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, and sometimes it can even save money.
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 (and arguably the cost of the items to prepare it) 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 at 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 (18" in most living areas and even higher in areas where they are expected to be at a higher height such as in the kitchen backsplashes, next to or over the bathroom counter, and in the ends of bathroom vanity cabinets or kitchens islands and cabinets), 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 the client or intended buyer - and there are many price points in these items as well, depending on size, style, and brand.