I've recently played Aurelion Sol a few times, and I think almost everyone can agree on something: Aurelion Sol depends absurdly on a specific item: Rylia's Crystal Scepter. And he isn't the only one. Though not all truely depend on the item, it is commonly bought as a dirty perma-slow item. Other examples of such champions are Azir, Kayle, Cassiopeia, Evelynn, Taliyah, Viktor, Malzahar, Zyra etc. They buy it most of the times, with the sole idea that 'Now my X ability will permaslow my enemy!'
The reason why this is not an issue on Frozen Mallet is a couple of differences.
Firstly Frozen Mallet gives a 'meh' 40 attack damage and 650 'nice' health. The problem champions with Rylia's are the damage dealers. Frozen Mallet's stat mix makes it more appealing to tanks then true damage dealers. Rylia's on the other hand gives 100 ability power, allot for an ap item. Tanks that buy Frozen Mallet commonly already have some CC or it is bought by bruisers, who typicly struggle to justify the item slot and gold for the Frozen Mallet, though they do desire it's passive.
Secondly the perma slow Frozen Mallet provides depends on your ability to attack a person with your basic attacks. Typicly, abilities have a greater range then ranged auto attacks, meaning on avarage it requires the Frozen Mallet user to be in a more dangerous position to apply it. Melee champions have an even harder time, though the stats do appeal them better then ranged champions. Because the slow is tied to your basic attacks, it means you only ever can trigger it on one champion realisticly. Ranged champions can use Runaan's Hurricane to slow up to three enemies, though again they prever stronger offensive items stat-wise, and they get dimished returns on the slow for being ranged.
But Rylia's isn't that bad as a whole. It is one thing, one game interraction that makes it flawed the most. Most of the earlier mentioned champions have an ability which is classified as an AoE, but the ability cooldown or trigger instances in Azir's and Aurelion Sol's case are so low. Those abilities should realy become classified as a DoT AoE and get the weaker 20% slow.
And then the nail in the coffin for the item is the dependency, as I mentioned to start the discussion, on a few champions. Aurelion Sol and probably Evelynn struggle when they are not in possesion of Rylia's, and become cheaty monsters when they do. And is very similair to the reason Riot had for removing the spell vamp on the Hextech Revolver and it's upgrade Will of the Ancients.
A solution could be to nerf some interactions with certain abilities or borderline exclude those abilities from interacting with Rylia's at all. A different way could be to make the slow a consistent 35%, but have it on a 5 second cooldown for each individual ability (or passive ability, mr. Brand and Aurelion Sol). Atleast those are my throws on a plausible solution.