Right now legendary items without greater affixes are kinda useless or only useful for a very brief period in the leveling process. But for this problem there is a
SOLUTION:
Simply add a new very rare consumable item to the game that can turn a normal affix on a legendary item into a greater affix. Example:
You have found the following legendary gloves without greater affixes:
Attack Speed
Critical Strike Damage
Critical Strike Chance
You think it has good affixes, but you are disappointed that none of them is a greater affix. So the item is basically useless currently. But here comes the idea.
Now you use your consumable item and you can chose the affix that turns into a greater affix. Once you find more of these consumable items, you can turn more normal affixes on this item into greater affixes.
The new consumable item can’t be used on enchanted items. And items that were improved by the new consumable, cannot be enchanted.
You can also use the new consumable that have only 1 or 2 greater affixes to turn them into items with 2 or 3 greater affixes.
Maybe this new consumable item could also completely replace the drops of items with greater affixes. It would lead to a much more flexible crafting of items.
Overall, the idea is to let the player chose which affix should be a greater affix. At the same time, all legendary items that are dropping can be useful again.
Right now, legendary items without greater affixes and even legendary items with only 1 greater affix are quite useless. My idea would make them useful again, because with the new consumable item you can turn them into legendary items with (more) greater affixes.
The idea can also be expanded to unique items. For example you need 5 times the amount of the new consumable to turn a normal affix on a UNIQUE item into a greater affix.
And finally this idea can also be expanded to mythic uber unique items. For example you need 25 times the amount of the new consumable to turn a normal affix on a MYTHIC UNIQUE item into a greater affix.
These are only example for the rules of this new very rare consumable item. Maybe it should drop in the pit. Or elsewhere. Or both. You can think of any rules surrounding this new consumable item that can turn a normal affix on an item into a greater affix.