If the most fundamental quantity in economics, price (P), is continuous and, therefore, infinite?
Why are economic models discrete?

The bigger question is why economists are biased toward discrete time models when time is actually continuous.
The answer, of course, is that the majority of economists are incapable of understanding a conventional differential equation, much less a stochastic one.
So everyone wins in econ: even the dullards feel like they are good at math, while anyone who does actually understand stochastic PDE at a remedial level is regarded as a genius.