I agree that time isn’t an input in the economic system.

Although, one can use either discrete or continuous time to simulate a complex economic system.

Only simple closed form models take time as in input, e.g. compounded interest or Black-Scholes.

Also, there are wide range of hourly rates/salaries, and not everyone compensated by time, some by cost-and-materials, others by value or performance (with or without risking their own funds/resources).

There are large scale agent-based model (ABM) simulations of the US economy, where you have an agent for every household and every firm.