I recently started playing Diablo3 again after taking a break for some moths. While playing solo I enjoy watching streams because they're sometimes really informative. Something I noticed there was that most streamers would first gather lots of legendaries before actually identifying them. I saw this behaviour at /r/diablo3 too, so I thought of any advantages this would have but the only thing I could think of was that you might always equip the best item out of a larger pool of items, but this seems to be only relevant to characters with a already pretty good item level. So why would people not want to identify their legendaries on fresh 70 toons? Especially if they have hundreds of millions of gold so that enchanting one semi-good item does not hurt them that much?
The group of people streaming for the most part know the game rather well. They know what the item is when it drops by its icon. Almost all of the legendary and set items that drop to one of these players is just going to end up as one Forgotten Soul of many.
So they gather them all up, and id them all at once so that they can go through and salvage them all at once. Items have their stats rolled when they drop, so there is no advantage to waiting to identify them. All the process does is show the stats, it does not calculate them.
This is just a time saving mechanism. I guarantee if they have one of the more rare items drop, such as Kridershot, Tasker and Theo, The Furnace, Stone of Jordan, etc. (the 1 in a 1000 drops) they will id it rather soon.
These players have a full set of best in slot items. Unless a possible replacement drops, it is probably useless to them.
For fun, I tried this out. I haven't been playing much lately, but since I really had no use for gear I collected a whole inventory and id'd it.
Unfortunately it was mostly useless and did not benefit from all being id'd at the same time. Overall, it resulted in a stack of Forgotten Souls.
No there isn't any benefit from waiting. Most streamers do that to build up hype on their stream like : Hey look I'm going to identify 100 legs on stream ! but it doesn't go further than that.
There is always the psychological aspect that when you identify more legendaries at once you feel you have more chance to have something good than identifying them when you get them but it does'nt change anything.
Answers to this question indicate that stats on legendary items are generated 'on drop', not 'on identify'.
It follows that when or how you identify looted legendary items (i.e. whether you identify them as you pick them up, one-by-one back in town, or all at once with the Book of Cain) has no effect on the identified item or its stats.
If speed is a priority, there is a practical advantage in taking all of your legendaries back to town and using the Tome: that it would take you less time to activate the Tome (5 seconds, from Wikia) than it would take to identify each legendary item individually (5 seconds per item, and with an inventory full of legendaries that'd take you at least 2-5 minutes.) And that's not even factoring in the time spent looking at your inventory every time an item drops.
Of course, theoretically you could pick up a major upgrade that didn't require enchanting or gemming, get a damage boost, mow through that rift a little faster and pick up more legendaries sooner... if you're lucky.