I’ve worked for not-for-profits. Profit is still a motivator. They need funds to operate. Obtaining funds, controlling budgets, it’s all part of the same thought process.

The only way to avoid profit as a motivator is to eliminate competition and provide fixed budgets. You will have X money to achieve Y goals. Your success depends only on achieving Y, and failure does not diminish your budget. Once you let profit in the door, it will seek out the people driven by it and plug them into decision-making positions.