Is there any reason why Q11 is left out on 4060 IC? I've read it was done to extend the max pulse time (highest clock divider) but why was it done on Q11? Why not Q12 and therefore have a full 8-bit counter (Q4-Q11)?
One possible cause for the design decision was that it was a packaging/budget constraint. They had the 4040 model which was packaged with 16 pins and they were able to manufacture a new counter with different features relatively easily by keeping it so similar:
The 4060 adds two extra digits to the counter along with two pins for directly connecting a crystal oscillator. So this would mean four extra pins. So to keep the counter at the same number of pins, they had to omit the output from some of the counter bits. It seems somewhat arbitrary to me which pins you would omit. The two MSBs of the counter seem to be the most important, since those two are one of the main features that differentiate it from the 4040 counter.
The 4040 provides a counter with a high number of bits (12) and no prescaler. The 4060 provides two different counters with different prescalers. There is a 6 bit counter with a clock/16 prescaler or a 4 bit counter with a clock/1024 prescaler.
In the end, the 4060 looks like it was designed to provide complementary features with the 4040. The 4040 doesn't have oscillator connections, where the 4060 does. The 4060 can divide the clock down 4x slower than the 4040 (the 4040 can be prescaled by /2, /4, etc by omitting LSBs). The 4060 doesn't provide a counter with a high number of bits, while the 4040 does.
I don't have any sources to back up my claims, so treat this answer as partial, and with some skepticism.