If your employees expect raises greater than inflation (like say 3%), or you're giving out any kind of healthcare benefits (that cost grows 10% annually on avg), or your rent goes up, etc etc, then you need to be growing in order to be steady-state.
Costs always increase -- staying the same size costs more next year.
In many businesses, employees become more valuable over time through experience such as skills acquisition and improvement, taking on more responsibility, training new staff, etc.
Even so, due to older staff retiring or leaving and newer staff joining at lower salaries, even if all staff have steadily increasing pay rates above inflation the overall payroll budget may still be in a steady state.
Most businesses look for ways to increase their margins over time, which will balance out increases in costs. If that fails, then they will increase their prices. Attrition should result in relatively flat total salary expenses (adjusted for inflation). As people leave, you promote (and give raises) from within the company, and hire new, lower paid staff.
No. For example, if one could reduce the cost of making widgets, and sell them at the same price, margins are increased without growth. This is a very common way that companies increase profitability.
Costs for supplies should decrease, and why would employees expect raises greater than inflation if the company is not growing or doing anything new?
Look at a McDonalds franchise, for a good example of steady state.
I don't see why costs for supplies should decrease, necessarily, even in real terms. I guess you can have consistent churn at a brick & mortar business to keep paying minimum wage by replacing people with younger people as they leave.
But that setup only applies if you're paying at the bottom of the scale and not giving out benefits. Bennies have been increasing by much more than inflation, and the type of jobs giving bennies typically expect a 4% raise, minimum, if you're doing acceptably at it.
A McDonald's franchise looks a steady state because that's the entire point. McDonalds is basically a holding company with a portfolio of some of the most valuable real estate in the world that uses the burger flipping as a way to constantly grow. However, no McDonalds franchise is a steady state unless its in a tiny town immune to inflation where no one wants to open a competitor (and there's very few of those). If a restaurant's profit falls behind inflation it's no longer as valuable a holding in their portfolio.
This delusion is why there are periodic economic crashes. It sticks around because if you are powerful you can take advantage of the thinking when times are good and skip the consequences when times are bad. When too many believe it's true, they allow it to be true.
The cost? An ever increasing chasm between powerful and powerless, a chasm which itself goes through periodic crashes which tend to be significantly more violent... e.g. the fall of Rome, the French Revolution, and WWII.
Costs always increase -- staying the same size costs more next year.