my primary obsession being pawpaw, Asimina triloba, this topic of taproots has been something i've thought a lot about.
Pawpaws are said to have strong taproots, and indeed if allowed to a seed will produce, for example, a 14-18 inch taproot or more before it even emerges above ground.
Many people recommend tall pots for seedlings to accommodate the taproot.
But some nurseries grow pawpaws in root training/pruning pots, or in open-bottom band pots that are only 5-6 inches deep. I have had some folks tell me with a very young seedling you can just whack the taproot off.
Like many things in the plant world, there seems to be no absolute on this.
However, i would not recommend cutting a taproot once it's already formed, at least not if the tree is actively growing (similar to HIFarm's experience). But it seems like you can likely successfully grow trees by inducing a truncated taproot from "birth" using air-pruning techniques.
I actually made my own "band" style pots this year with depths of about 8 inches, in which to grow pawpaws. The seeds behaved just like every other pawpaw i've grown, and the trees are plenty healthy. I've planted them in the orchard, so time will tell of the long term impacts. (I also have a commercial-grown pawpaw with about a 5 inch taproot that made it fine through its first year and is growing vigorously now in its second spring in the ground. But in the back of my mind I feel i need to keep an eye on it since its root system was so small initially.)