Engineering decisions are fundamentally about problem solving. Thus, when asking, "Why not do [x] instead of [status quo]?" an answering question is: "What problem does [x] solve or what benefit does [x] provide versus existing designs?" If no satisfactory answer is forthcoming to the second question then that's the answer to the starting question, i.e. [status quo] is a better engineering solution.
When assessing a proposed solution, considerations include: safety, constructibility, initial cost, life-cycle cost, maintainability, aesthetics, etc.
So, how do pavers stack up against existing roadway toppings like asphalt concrete? Overall, I'd say not great. It's likely a more expensive material from the get-go, more expensive and much more laborious to construct, less maintainable, and less safe (the uneven surface issue you identified). Note that roadways are often carefully cambered and banked to ensure proper drainage and safe driving dynamics, so we have the added challenge of actually not wanting a perfectly level surface, but rather a smooth surface that is sloped in a precise way.
It could be argued that stone pavers offer an aesthetic benefit, but the driving surface aesthetics are a low priority for major roadways so the pavers aren't offering much value versus existing engineering solutions.
On personal property like driveways, the aesthetic consideration may be much more significant to the owners, and low driving speeds plus a small project size change the value equation appreciably versus a highly traveled roadway.
From a more big-picture perspective, it's interesting to know that the actual driving surface is only a small part of roadway design. Furthermore, pavement design actually is an active area of Civil Engineering research. I myself am not a roadway or pavement engineer, but having worked with those folks on various projects I can confirm that roadways are carefully designed, both in terms of geometric layout and the 'structural section' that generally extends much deeper than than the final paved surface you can see. An example roadway cross section from the California Department of Transportation Highway Design Manual is included below for illustrative purposes.
Ultimately, I think we can say pavers just don't make the grade for major roadway applications, but innovation in pavement engineering is certainly something engineers and researchers are striving for!