Also, Grey gear starts with no secondary stat. Green gear stars with one secondary stat, blue with two secondary stats, and purple with three secondary stats.
If secondary stats are determined randomly when upgrading, starting with purple gear with three secondary stats that you want will allow you more control over the final stats. As others have said, it may also allow you to take the secondary stats higher than if you started without them.
I guess a purple 5 dot with the particular stats you want will be extremely rare.