The smaller the employee turnover and the longer workers work.If there is money to be made, employers will employ and will do so regardless of worker protection.
This bolded part is the key assumption. Only if an employer can be sure that hiring an employee will increase their own profits, will they be sure to hire them.
Such certainty is less common outside large companies with massive volume and thus rather predictable demand for their product, and where the skills required to perform the task are minimal.
If demand for my product in uncertain and variable, and the ability of any employee to do the work is uncertain, then hiring them could easily lead to a loss in profit. If the employer cannot fire them if and when they turn out to cause profit loss, then the employer will sometimes not take the risk of hiring them.
Adding labor is necessary but not sufficient to increase profit. There must also be a demand for what that labor produces and the ability for that labor to produce what is demanded at a lower cost than the price its sold for. These extra factors make adding labor a risk - reward decision. Being able to fire whenever those other conditions are not met and the labor leads to profit loss lower the risk of hiring and thus increases the decision to hire in situations where the reward of doing so is not certain.
That said, requiring notice still keeps risk relatively low and thus would not reduce hiring.
In sum, without being able to fire at will, Wallmart and McDonald's would still hire as many people. However, but a mom-and-pop shop with 1-2 employees whose business is picking up but could drop at any moment would wait to hire until it was more certain that they are losing potential $ and will continue to do so unless they expand their labor.
I support many things Unions do, but the only area where preventing at-will firing makes good sense are those public sector jobs where there is little change in a downturn in demand/need and where being fired for unjust political or personal agendas unrelated to competence and productivity would otherwise be common. Teachers and scientists in the public sector are the most obvious candidates that meet these criteria, which is why tenure makes the most sense for them.