Morde is the only champion that has neither mobility or CC. I think that just sticking mobility or CC on him would homogenize him in a bad way, and I don't agree that mobility and CC are the only options to make him more playable. I think that he could be made even less mobile by giving him more channel abilities or cast times, but he could be made much, much tankier, and he could become more reliably useful in other ways.
For example, his E could be reworked so that Mordekaiser collects souls when nearby units die, and souls would permanently upgrade his E. Casting his E would lock him in place as he channels to release a replenishing stream of souls, which would spiral around him, dealing AOE melee-range AP scaling magic damage around Mordekaiser, and then would follow his cursor at a decent projectile speed for a couple seconds before dispersing in a random direction (slightly similar to a constant stream of Heimderdinger rockets), dealing a small AOE of damage if a soul collides with a target. The total number of souls summoned and rate that they stream from Mordekaiser would depend on his E rank, number of collected souls, and how long he continues to channel his E.
His Q could be updated to deal AOE damage like it did in a previous Mordekaiser version. Rather than a 3-hit effect, it could become a free-movement channel combo, where he swings his mace several times in a wide horizontal arc in front and beside him, locking him into a target orientation but allowing him to continue moving (like Taric's stun targeting), with additional AOE "lighting chaining" from any targets hit. The chain lightning would let him more reliably deal damage to multiple targets in teamfights as long as he can close in on at least the enemy front-line. The upfront damage could be physical, scaling with AD, and the chained lightning could be hybrid scaling.
His W and passive could be updated to scale incredibly well with tank stats to encourage tankier juggernaut builds. Because he doesn't provide utility, he would still need to build some damage in order to be useful. His W damage could scale with both resistances and AP; this would allow him to build tanky early on, but it still shouldn't allow him to reliably build full tank (adding a high AP ratio on his ult and E should ensure that). The "magnet" speed boost could be removed and the healing could also be removed and replaced with just more shield generation and temporarily increased resistances during the W effect duration.
His R could immediately tear a shadow of his opponent's soul from its body, creating a corrupting phantom that deals bonus DOT damage if used against the original target it was pulled from. If the original target dies, the shadow would become more substantial and its bonus DOT damage would then apply on all other targets. The current live version's ult's mark DOT would be removed since it would be replaced by the new bonus DOT that the phantom can apply while in combat with a target. The phantom's stats could derive roughly 50/50 from the enemy target and Mordekaiser, health, resistances, AD, AP, and attack speed being averaged between Morde and the target. It would deal physical on-hit damage scaling with its total AD and it would deal magic on-hit damage + magic DOT scaling with its AP.
With this rework, Morde would be even less mobile in combat because of his E channel, but he would feel more reliable at outputting damage with his E's higher range and Q AOE splash range making him less likely to be completely kited (to nullify him, you'd have to avoid the zone he's in altogether, which might mean giving up objectives). He would feel like an absolute boss, being nearly unkillably tanky and outputting team-clearing AOE damage if he manages to corner a team in the dragon pit for example, but he'd be so slow that it should be possible to outmaneuver him to try to separate him from his team. He would be able to easily clear minion waves and jungle camps, but his immobility and lack of CC would make vulnerable to being collapsed on if he tries to split push. He could have incredibly high scalings which would justify a weak laning phase so that he doesn't play as a total lane bully against other melees. His power curve could have him start very weak, usually losing his turret and being pushed into his base, but his high pushing power would scale up and allow him to repel the waves and begin to comeback as he scales into a complete titan who should eventually feel invincible but avoidable, but who also creates such a large threat zone around him that his team can get a lot of advantage from playing around his presence.