What are the cons of two-factor authentication?

As a concerned user of online services, I'm curious to understand the drawbacks of implementing two-factor authentication. While it's widely regarded as an added layer of security, could there be any potential downsides to this practice? For instance, might it lead to increased inconvenience for users, particularly those who frequently access their accounts from multiple devices? Additionally, are there any concerns around the privacy implications of sharing additional personal information or relying on third-party verification services? It would be helpful to gain a comprehensive understanding of the potential cons of two-factor authentication before making a decision on its adoption.