There is conflicting information all over the internet about regrowing carrots from tops. I know you can grow the greens, however, can you grow the actual root vegetable again? And if not, what is the scientific reason why not?
Yes, you are correct that you can cut off the top of the carrot and regrow the leaves only. Once the taproot (carrot) is removed it cannot grow another.
When cut from the top, the growing point for the taproot is removed, however the growing tip for new leaves is not removed. The growing tip (meristem) that forms the leaves can also grow new adventitious roots (fibrous roots), but not a taproot.
You would need to allow the top to flower, go to seed, then plant the seeds in order to get another carrot with a taproot.
See photos on this science snacks page about how the vegetables can start growing again.