Why Mordekaiser doesn't work, but Rumble does
So, a few days ago I made a thread detailing how Mordekaiser doesn't fit in with the other juggernauts-- mostly in ways unrelated to the fact he was arbitrarily kept mainly AP despite no items being created/adjusted for him during the jugg update three years ago. You can see it here https://boards.na.leagueoflegends.com/en/c/gameplay-balance/g7210pEU-so-when-are-they-making-mordekaiser-a-juggernaut
Now, it's clear Mordekaiser and Rumble are intended for different purposes, but Mordekaiser is far more similar to Rumble than he is to the real juggernauts, both in play style and build (in play style mainly because of the build). They both try to remain pretty close to melee range, using Rylai's to keep the enemy near enough for Rumble to Q/ Mordekaiser to E-- and Q if he's lucky.
They're very different champions aside from that, too, but the difference that makes Rumble a consistently strong pick while Mordekaiser suffers is that Rumble can roll with changes to Rylai's and Liandry's far better than Mordekaiser can. The fact his main damage ability is DoT means he can more consistently apply both items, whereas Mordekaiser must rely on his E most of the time just to slow the enemy. On that note, Rumble has his own slow with double the range, duration, and slow of Rylai's-- which is Mord's only method of cc'ing the enemy. And now that single-target damage slows just as little as AoE damage used to, Morde's Q gives him no bonus to the slow amount. Rumble's ultimate is also AoE and slows for more than Rylai's, allowing him to hit more targets and keep them in range of his Q, and even put off building Rylai's at all. Whereas Mordekaiser's ultimate is only single-target, and requires Rylai's to get the extra damage from Liandry's. The fact it heals him for only its own damage serves mainly as a crutch preventing them from giving the ability any meaningful damage adjustments.
In short, Mordekaiser is completely at the mercy of Brand's effectiveness with his core items, while Rumble can overcome changes to their core items with his more versatile kit.