The wider the aperture the more difficult it is to correct for aberrations that reduce sharpness/contrast etc.
When you stop down a fast lens these aberrations simply go away, as you are physically blocking the light that is causing them.
So designing an f/1.8 only lens, is exactly as hard as designing a variable aperture lens with maximum of f/1.8 (plus the minor difficultly of including an iris). However the f/1.8 only lens is much much less useful, for pretty much exactly the same cost, which is why nobody does this with interchangeable lenses.
Early lenses were designed with single apertures as you suggest, but these lenses had a slot into which you could insert pieces of metal with different sized holes to obtain different sized apertures. What you are suggesting is something like this lens, but with the slot glued shut so no-one could use it. Gluing the slot doesn't make the lens cheaper or improve performance in any way.
Some fixed aperture lenses do exist, such as the "lens in a cap" or mirror lenses. Most such lenses have a property in common, they have very small apertures like f/8. In a sense these lenses are already stopped down, adding an extra stop or two wouldn't make much difference, in the case of mirror lenses they are almost always long focal lengths where stopping down would make the lens unusable due to camera shake. For the lens in a cap, well it's a toy lens, adding a variable aperture wouldn't make it into a serious photographic tool, so why bother.
Other lenses that have fixed apertures include camera phone ultra compact cameras. These have sensors that are so small stopping down would cause problems with diffraction.
Finally most scientific, industrial and medical lenses have a fixed aperture as they are designed for a single purpose, so the aperture is fixed at the correct value for that purpose.