For consistency, I think all plants should remain sorted by their botanical name in all lists. If the lists arbitrarily switched from sorting by the botanical name for most and the common name for some, it would seem to just become a mish-mash. The garlics should list with the other alliums, etc.
Another thing that struck out at me when scrolling through My List is the simplification of certain genera looks (to me) like we don't know what the botanical name is. An example is the crocosmias. Since the common and genus name are the same, you have eliminated the italic genus name. When quickly scrolling down, that jumped out at me as missing information.
I think consistency and accuracy is more important than the perception of redundancy - edited to add: Allium sativum 'Burgundy' (Garlic) conveys more accurate and useful information to me than Garlic 'Burgundy'
