char buf[LINE_MAX]

Why do programmers still code in arbitrary limits like these?

It breaks when you do
#define LINE_MAX UINT_MAX

Why not redesign so that you use an O(1) space algorithm, or if it can't be avoided, dynamically allocate as much as needed?

Let's clear this up once and for all. Dynamic languages such as Python, Ruby, etc, all will malloc the memory when you do a readline, so there is no reason why you couldn't/shouldn't do it in C.