All the cotton here in Aus is pre-shrunk. But t-shirts tend to change shape (I’m not sure if this is only after being heated in a dryer). They get shorter and fatter.
Why is this so? Why not longer and skinnier? Is it something about the way they are woven, or do you think the observation is just wrong?
T shirts are knitted, not woven.
Knitting, as I know from sad personal experience, tends to stretch vertically (perpendicular to the rows) and contract horizontally (along the rows), just from the weight of gravity.
Washing causes the stretched-out stitches to ‘bounce back’ to their original form. The T isn’t exactly losing length - it was knit shortish, and it stretched to its apparent length afterward.
The bounce and the stretch are more extreme when the fiber itself is less elastic, counter-intuitively. Wool stretches out less because it is elastic and ‘bounces’ back from stretching by itself. Cotton has very little elasticity to ‘bounce’ it back its original shape. Washing it adds temporary external elasticity through the action of the water.
Also, the cotton threads themselves may shrink a bit if they were not pre-shrunk before knitting. if this is the case, the item will lose both length and width, but more length, because length experiences both effects.
Thank you for the explanaition 
To get the lengthening effect on purpose, you can hang the knitted object to dry, instead of tumble drying. Gravity will cause it to stretch vertically. The actual thread in the stitches themselves will stretch a little, and so will the rows due to the loops moving vertically. Don’t forget that the item will also pull in horizontally.
Putting a light weight on the hem will increase the effect. Experiment cautiously with weight. For most items you only need a few clips, or at most, a few clips with a washer or two hanging off them.
Cotton, linen, ramie and other plant fibers will stretch the most and stay where they are stretched to the best. Wool can be re-shaped this way, but will tend to revert to its original shape in time.