Leaking a monotonic ID could allow outside observers to estimate e.g. number of accounts created or products sold over certain timeframe. Competitors (or traders, for a public company) could use this like a form of inside information on the company (e.g. sell the stock if the rate was falling).
This would really only be possible if you leaked a monotonic sequence; the monotonic clock only would potentially leak only event ordering or absolute time.
IMO it's not the job of the identifier itself to prevent information leakage vulnerabilities though; if thee is sensitivity to this, the solution should be explicit, such as employing a secondary key derived from the UUID using a secure KDF or similar.
