tl;dr: NP-hard problems are widely misunderstood as intractable, but in practice worst cases rarely occur and modern solvers routinely find provably optimal solutions—Amazon reportedly solves a billion SMT problems daily. Algorithmic improvements have outpaced hardware gains, with one paper citing a 450-billion-fold speedup between 1991 and 2015. When worst cases do hit, engineers can handle them the same way they handle slow HTTP requests: timeouts and error messages.