Rylai's Direction (Replace Rod of Ages)
TL;DR Remove Rod of Ages and make Catalyst built into the new Rylai's. . . . First of all, let me begin by saying that I'm a little tired and just throwing out some gut feelings that may or may not be well received. Gon' rant.
I don't like Rod of Ages. The item feels very much like a stat-baton that is supposed to start out weak and turn out strong, forcing people to play kind of safe for a while then spike. I mean it is kind of a cool concept but in all reality I find that is is hard to balance and is a fairly uninteractive item that simply pushes out other options.
If you want to buy it, you have to buy it first item. That does not lend to diverse itemization. If you buy it on an AP champ, I feel that there is an overwhelming need to buy Seraph's just to get the best value out of ROA. Feels bad. If it scales better than other items (considering it gives a lot of AP), then why buy other items? If it doesn't scale better than other items, it is worthless. It gives a lot of generalist stats and makes people tanky when it probably shouldnt...
Champions that like the item (according to Lolking):

Champions that SHOULD like the item (people who kinda need health and want some mana/ability power):
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Moving onto Rylai's, this item has become sort of a no-brainer. It is a big ticket AP item that offers health and massive kiting/chasing power.
This combination makes Rylai's much more powerful than alternatives because it nullifies a lot of these champion's weaknesses while exploiting the weaknesses of others without significant trade-off.
Champions that like the item (according to Lolking):

Champions that SHOULD like the item (people who need the kiting/chasing power):

. . .
Now, I'm not really saying that the people who like the item shouldn't or that the people who should like the item don't. Moreso, I want people to look at the two champion pools I listed and notice similarities between the two. There is a LOT of overlap between champions that do/should use Rod of Ages and Rylai's. This is what leads me to think that maybe some of the issues surrounding the two could be resolved by finely tuning a combination of the two items.
By getting rid of Rod of Ages and making Rylai's build out of Catalyst and an AP item, you could get a fairly niche item that is actually picked up by a lot of people for different reasons. (Not sure if it would still be niche...) OH, AND GUESS WHAT. Since this is supposed to be a sort of time-based item, with ETERNITY being a thing, it would make sense that perhaps the item would SLOW YOU. You know, like, it lasts forever, you're slowed forever? Half a bad joke, half still a bad joke.
EX: Rylai's Aged Crystal Rod Built from Catalyst and Blasting Wand +500 Health +300 Mana +60 Ability Power UNIQUE – ETERNITY: 15% of damage taken from champions is gained as mana. Spending mana restores 20% of mana spent as health, up to 25 per cast (toggle spells heal for up to 25 per second).
UNIQUE Passive: Damaging spells and abilities apply a Movement Speed reduction to enemies based on the spell type: Single Target: 40% reduction for 1.5 seconds. Area of Effect: 40% reduction for 1 seconds. Damage over Time or Multi-hit: 20% reduction for 1 seconds. Summoned Minions: 20% reduction for 1 seconds.
(If a spell fits in more than one category, it uses the weakest slow value.)
Seems like it would be good, situationally, on:

Because it offers some of what all of these people want, but it's not perfect for any one person at all times.