They do understand that cutting costs will have an impact on culture and morale, they just think the marginal benefit exceeds the marginal cost. Keep in mind, PEG managers are chasing a carried interest bonus which they only achieve after covering the minimum return promised to their investors. Plus, leveraged buyouts--which PEGs frequently use--increase a company's risk of failure. Everyone's under intense pressure to perform.
Massive Financial Incentives + Highly Leveraged Balance Sheet + Intense Pressure = Risky Decision Making