In practice if you fired people weekly/monthly/quarterly (pick a small enough discrete period to approximate “continuously”) at % you wouldn’t be maximizing profits due to other costs. “Non-linear effects” is carrying a lot in your description.
Take a high performing team, fire them, and then rehire tor it, retrain, etc. the cost it took to get to the previous level of productivity is the “knowledge capital” that was squandered. It usually will be more than the labor savings, unless we are talking about huge disparities based on decades of seniority: older workers with higher pay and defined benefit pensions etc vs younger workers with defined contribution pensions, is about the only case I’ve seen this make sense, and it was a once-in 30 years kind of thing.
Then there’s the reputation and morale hit: people won’t want to work for you if you have a reputation for regular layoffs.
Amazon for example is struggling with employee turnover and morale because of its aggressive approach to annual PIP and layoffs.
Labor costs also tend to be sticky downwards - people will accept getting laid off but won’t accept a pay cut.
Of course there are industries with seasonal or overflow workers etc where this is an understood job characteristic, but that tends not to be the norm…