What is the evolutionary reason behind the fragility of teeth?
The evolutionary biologist in me would argue that, on average, teeth are exactly as strong as they need to be. In other words, the fitness cost of producing and maintaining teeth is balanced with the the fitness benefits of having teeth.

To address your questions from an evolutionary lens:

Why haven't humans evolved in the past tens of thousands of years to the point where repairing or regrowing teeth by natural means is feasible? Simply put, why don't teeth grow back contrary to hair, nails or skin?

The short answer is that we have evolved the ability to regrow teeth. That's why you lost your baby teeth and a new set grew in their place. And why most folks have wisdom teeth that grow in later in life.
Essentially, we only need enough functional teeth to get us to the point of reproduction. After that, the effects of selection for stronger, more, better teeth wanes. 

You may find this review article1 helpful wherein the authors explore the evolution of teeth, and specifically health issues related to teeth from an evolutionary perspective.



[1] Koussoulakou et al. (2009) A curriculum vitae of teeth: evolution, generation, regeneration. Int J Biol Sci; 5(3): 266-243.