I have noticed in all the books as an introduction, it is written that the Fan out is one of the performance measurement parameter for the Logic families.
Why do not we look at the Fan in ?
When you see fan-out... I expect there is also fan-in mentioned.
Before CMOS there was TTL. TTL needs a lot of input current, but nowadays CMOS input current is about zero.
But there is some input capacitance ... this is what degrades signal performance.
Fan-in other than 1 is only occuring in special cases where a pin is directly driving multiple internal gates without buffer. If you read the books thoroughly, you'll notice that fan-in has much less general importance. Particularly it's no performance parameter.