The Chinese Tallow tree was introduced to the United States during the 1700's, and since then it has made itself at home throughout the southeast coastal states. It is now considered an invasive species by the state of Florida and is illegal to propagate and transport. In some areas the trees are notoriously difficult to remove, being known to successfully re-sprout from stumps and forgotten seeds. It grows very well on lands that are unsuitable for row agriculture, like, oh, most of Florida. It has naturalized itself in some areas, displacing native plants and animal habitats.
It was originally introduced for commercial production of natural vegetable oil from the white seed coats, but industry never really took off. Perhaps it is too difficult to remove the seed coats from the fruit. An easy to grow natural vegetable oil would be a great crop for the South if it were viable. Popcorn trees are largely unaffected by pests. It attracts bees and butterflies. Birds and squirrels eat the fruits, reluctantly, if there isn't anything tastier to be found.
I think the seeds would have a good use in starting campfires as a kindling, if you are a fan of cooking or relaxing with a campfire. Being naturally high in oil, they should work quite well for that purpose. It also will prevent the tree from reseeding all over your yard.
The leaves change a range of beautiful oranges and reds in the fall, which is one of the reasons it formerly was planted nationwide as an ornamental. This quality and it's fast-growing nature would make it an excellent specimen for a bonsai practitioner, being mindful that it is illegal to propagate. Then again in Florida gardening is only illegal when it bothers someone else... so a well-maintained bonsai (with prompt fruit removal) from is unlikely to cause trees sprouting in the neighborhood.
The milky white sap of the tree is toxic, like all other plants with milky saps. Please be careful when handling parts of Popcorn tree, and avoid sap to skin or eyes contamination.
The seedling problem is largely overstated here in West Florida where we have very distinct dry and wet seasons. There are maybe 10 to 30 Tallow trees here in this town, and they all appear to be about the same age, which leads to the idea that perhaps they all came from one nursery about 25 years ago. There are no seedling trees here to be found, possibly a side effect of frequent urban mowing.