The problems are exactly what you describe, with ensuring that transport will not ruin the fruit. Another facet is not only that the tomatoes are picked unripe, but also that the varieties that are grown are ones which optimize for being able to withstand long transport times as well as for uniformity. Consumers as a group like uniform, smooth, red-colored tomatoes, and they like them year round. Flavor, aroma, and texture are sacrificed.
I can pick unripe tomatoes from my vine just as they are turning light green. They will ripen in the sun and will have a lot of flavor (although maybe less sweetness). Picking them green is not 100% of the picture. The types of tomatoes grown plays a big part.
If you have a chance, buy some heirloom varieties from a local food market or a farmer.