That's a lot of fancy sounding words to say something that is obvious to any programmer. Big O algorithm analysis assumes that input size increases indefinitely

That's a lot of fancy sounding words to say something that is obvious to any programmer. Big O algorithm analysis assumes that input size increases indefinitely. However, in real world problems the input size usually has a natural upper bound. As long as you can write a fast enough implementation (exact or approximate) for the largest conceivable input size, the problem is tractable. All algorithms designed for a bounded input size are technically O(1). Even reducing it to SAT and invoking a SAT solver is too much. Most of these problems are solvable with simple enumerative recursion with optimizations like memoization, backtracking, and branch-and-bound. For example, airline computer systems solve NP-Complete problems on a daily basis.