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Ofcourse, we're all free to have our own opinions on the matter of what to prefer. And yes, Ryze should without doubt have the Archangel's Staff, just as you say.
Lux can benefit from it too, depending on runes and masteries. Given her AP is high, it should be high for a reason, namely casting spells. Since her spells tends to be expensive and especially in the earlier parts of the game, then maybe not an Archangel's Staff early on, but a Chalice of Harmony as a supplement to the staff which will later on be exchanged for the real thing.
If you're going for a glass cannon build, then I'd definitly go for this build on Lux, taken I make it to a full build:
Mejai's Soulstealer, Sorcerer's Shoes, Rabadon's Deathcap, Archangel's Staff, Archangel's Staff and Rylai's Crystal Scepter
Let's start counting, shall we? Let's say everything is fully stacked for this case:
Mejai's: 20 + ( 8 * 20 ) = 180
Archangel's: 45 * 2 = 90
Rylai's: 80
Rabadon's: 140
Total, without modifiers: 180 + 90 + 80 + 140 = 490
Then, her total mana pool would be at (Lv18): 1150 + ( 400 * 2 ) + 1000 = 2950
Take her mana pool, and convert 6% into ap: 177
We're at 667 ap at this moment.
Now multiply the total ability power with a factor of 1.3 due to the Rabadon's Deathcap's unique passive:
667 * 1.3 = 867.1
Note that no runes or masteries have been counted for. I think a double of archangel's is absolutely valuable to a mage. The only thing that DOESN'T stack on a double of archangel's is the increased mana that caps at 1000.
However, I might consider a Rod of Ages instead of Rylai's Crystal Scepter to gain even more mana for my Archangel's Staffs to convert. Plus a bit of health.
Therefore with only one Archangel's Staff being built if you have 2000 mana you are only converting it to 60 AP which can be found in better items at least for Lux
I'd like to both agreed and disagreed with you a little here. You're right up until one can add personal favorites of items (Zonya's, Abyssal, RoA). In my opinion, the Archangel's Staff is a have to, preferably more than one. Concidering that the effect of 3% of your maximum mana is converted into AP is not a unique passive, so it stacks if you have more than one.
This means that if you have one Rabadon's Deathcap and five Archangel's Staffs you will have 4150 mana (taken that the UNIQUE passive is maxed and Lux is Lv18 ) of which you will have 15% of converted into AP. Also, with the Rabadon's Deathcap that gives you 140 ap and also multiplies your AP by a factor of 1,3 is IMMENSE!
Start calculating the ability power and you land on a stunning 1 284 ability power!
Needless to say, the Archangel's Staff is more to a mage than just mana. However, the odds of having 5 of them, sacrificing boots, spell penetration and tons of cooldown reduction is slim to none. But I still always include atleast one in any of my builds as a mage.