Honestly, I don’t find that explanation helpful or accurate. I don’t think Compatibilism says we need to pretend we have free will. It says we do have free will, just not the metaphysical kind that most people want.

I'd add that generally, compatibalists don't believe that libertarian free will is the kind that most people want.

Most people believe in free will, most people also believe that their actions follow from prior causes, and most people also believe in moral desert, so most people are definitionally compatibalists.

The typical framing where people are asked to go back in time and imagine redoing past events without memory of the future pumps their intuition for time travel fiction where doing things differently is the entire point of the scenario. If you ask people "if everything happened exactly as it happened, could you alter the past to change the future?" most people would say no.