Uh, that's what the theory people do, too. We make assumptions about the model, for example, that if our input is of size n, a machine word should be able to st

Uh, that's what the theory people do, too. We make assumptions about the model, for example, that if our input is of size n, a machine word should be able to store that number (word size θ(log n) bits). Otherwise we'd never get anywhere with asymptotic analysis. In my experience, practitioners just have a lot of misconceptions about "Big O".