Yeah, that's pretty much the canonical model. Huge in the 80s for a variety of reasons, still extremely common today.
There are other models for PE and going private- sometimes companies don't use nearly so much leverage and are effecitvely bought as part of portfolio, sometimes you see very rich individuals take their companies that they used to own private again, sometimes they do use tons of leverage but buy and run the companies mostly as is, just growing the company in place and paying down debt from cashflow.
PE's and LBOs aren't necessarily bad things at all and the economy as a whole is better for having them exist. The problem is that the risk/reward profile tends to exaberate inequality. The PE/LBO firm is already rich individuals who may make our lose millions on a bet on the company. The control their own risk and decide. The workers and communities who also have a stake in the company? They have very limited upside and the downside is that they lose their jobs and anchor institutions in their communities, and they have very little control over whether or not to accept the risk.