Why Seeds?
Seeds are far simple to harvest, store and transport.
Harvest
Seeds are created by allowing the plant to flower, cross pollenating for some plants, and then allowing the plant to seed. To harvest simply collect the seeds as the seed pods are opening. There is nothing simpler and left to their own devices most carnivorous plants will sprout seedlings around themselves.
Storage
Storage changed depending on the plant with the majority of plants simply need to be dried, placed in an air-tight bag and refrigerated.
Since harvesting and storage is so simple, growers can grow far more plants than they have space available. Given a small growing space a CPer can grow several species by cycling the species they grow, harvesting the seeds from one season to re-plant again in few years.
Transport
Plants, mature or otherwise, are difficult to ship as they require more packaging that not only protects the delicate plant but also keeps it moist. Delays in transport or even rough treatment in transit can kill plants. Most importantly, the restrictions on the import and export of seeds is much lower than plants. For instance, many localities require certification that the imported plant is free of pests and may require further quarantine. Seeds are almost universally exempt from these restrictions.