I'm assuming this is for larger/later rounds so that YC can invest in their very successful companies (think Airbnb and Dropbox), and not for Series A/B companies.

YC does follow on investments but they are done by partners today. Negative signaling exists but it is swept aside because it is not a YC fund following on. Now they will have a large fund to do it so will be interesting to see how they navigate this landscape.

What if they added in a right to invest a certain amount in future rounds, such that they don't lead the growth?

They don't want to do this, because they don't want to become a "stamp of approval" for companies coming out of YC.

Specifically, if a company comes out of YC and is looking to raise further funding down the road, it becomes an important data point if YC decided to continue investing with them or not. By not participating in future rounds as a policy, they avoid this potential issue.

Why is it important not to pick favorites? Are they trying to avoid killing companies they thought were bad but end up good later on?