This is what I found:

"It is a valued ornamental tree with large foliage and showy clusters of flowers in the spring. When grown as a specimen many gardeners drastically cut back the large branches of their catalpas each winter. This radical surgery is called pollarding and the result is a tree with a thick trunk, very compact crown and very large beautiful foliage."

Here is a link that might be useful: More info

i was thinking along the same lines as the reason mentioned in terramadre's post. perhaps in the same way people keep their crape myrtles pruned, they view the unnatural, thick heavy form as attractive. beauty is in the eyes, i reckon.
wonder if it could have anything to do with reducing the mass of the canopy to facilitate harvesting the catalpa worms for fishing bait? people tell me you can freeze them to use when they are not always available. those would be serious fishermen to do all that for some bait!

I think Jeff is right about the caterpillar harvesting. It brings them all within reach.

Yes it brings the worms within reach for easy gathering. I had a old timer tell me the best time to cut the trees back is very early spring, after danger of freezing but before the leaves start to bud out. He said the freezing of cut limbs stunts the tree. He also told me not to use a chainsaw because of the oil off the blade, cut them with a hand saw.

Hi Jeff_AL,

There really are some serious fishermen out there. My brother in law (deceased) ran a bait shop for many years. He owned land where he kept a large number of Catalpa trees just for harvesting the caterpillars. I used to help him harvest them! Better wear a hat and long sleeves, you'll get brown stuff all over you :~). He kept them in containers with a dozen caterpillars each in deep freeze for off season. His customers were very happy to find them and paid high prices for them. Ed made lots of money, so everyone was happy.

Some of us are strange and actually like the stubby, unique look of a pollarded catalpa tree..:-)