Why do manufacturers specify typical values, not just maximum and minimum?
It is not standardized how often typical values actually are seen in your parts.
But many datasheets also show histograms of the distribution. For example with your TL081 it is in Figure 6-1:

This histogram can help you to decide wether it is worth choosing this cheaper part compared to a more expensive one (you just might have to do production testing and sort out the few chips that fall outside your tolerance range).
But be aware that these histograms often are no guarantee either. The maufacturer may have a footnote explaining that the distribution comes from just one manufacturing batch and the distribution may vary at other days.

There are several reasons why a manufacturer might want to specify a typical value additional to the min/max values:
It might be just a marketing &quot;trick&quot; to be able to show some nicer values.
But in other cases it is just that guaranteeing e.g. a max input bias current in the fA range is extremely expansive in terms of testing. If the manufacturer gives a max value of 10fA he basically has to test each an every part to comply with that spec. This intensive testing increased the price of the part. If the manufacturer just does some basic testing the part can be sold to a lower price. Then the max rating can say something like 1µA, while in reality 99% of parts fall within the typical range of 10fA.