The reasoning behind this seems to be that Aspects from MeadeDorian's blog

Yes, it does make a difference: extracted Aspects are generally stronger than the versions you get from clearing a dungeon for the first time D2R ladder items. The Aspects added to your Codex of Power will always be the weakest version of the Aspect, while those that drop from enemies or that you collect from the Purveyor of Curiosities have a chance of rolling higher stats or multipliers.

The reasoning behind this seems to be that Aspects acquired from dungeons are guaranteed drops. So, providing you've got the gear to imprint the Aspect onto, and the gold and materials needed to complete the action, you'll get that powerful piece of gear. If you want a potentially more powerful Aspect, you're going to need to kneel before the RNG gods and start farming those drops.

It's also worth noting that you can also find Aspects that are only available from drops, so if you want to move these to a better piece of gear, you'll have to extract them first.

When upgrading Legendary Weapons and Legendary Jewelry you need some very specific extra materials, and these are Baleful Fragments and Abstruse Sigils respectively. Both have a pretty appalling drop rate, so it's understandable if you've never gotten any, but in order to get them you need to dismantle Legendary items. Baleful Fragments have a chance of dropping when you dismantle Legendary Weapons buy d2r items, and Abstruse Sigils, when you dismantle Legendary Jewelry.