Does the Use of a Private Mempool Negate the Need for a Commit-Reveal Scheme?

For most purposes, yes. A private mempool allows a user to submit a transaction directly to a block builder/validator without it being broadcast to the public mempool.

Since MEV front-running relies on observing transactions in the public mempool, a private mempool eliminates the information advantage. This achieves the same goal as commit-reveal (hiding the order) but with much lower latency and cost, effectively negating the need for the two-step process.