Where you see "versatile" I see "confused". Not that it's bad to have alternate builds, but there's a fine line between champions who are good with many different items like Jax and Kayle and champions who demand a lot of things just to function like old Sion.
Morde likes quite a mix of things. He scales so well with AP and AD, he's melee and short ranged so he'd love tanky stats, he can make use of attack speed but not so much crit, and he loves some sort of slow from his items. He's also one slow bastard, even compared to other juggernauts. So movement speed is key. That's quite a bit to ask for, especially when so many champions are only required to build half of those things or less to be competitive. Even if you go only AP or AD Morde, you still need some defensive stats and also pen items to make up for losing the mixed damage of a hybrid build.
Compare him to Jax, who likes all those things Morde does. On the other hand, Jax gets free attack speed, tank stats, damage mitigation, and mixed damage from his kit. Jax can also be quite mobile if he wants to be and has hard cc, making movement speed and slows from items less important. He can still build those things if he wants, but it's not a big deal if he skimps on some things.
Morde does get a shield built into his kit, but it scales with defensive stats; the very stats the shield should mitigate you skimping on. The rest of Morde's kit is damage, damage, and then damage. Anything Morde lacks (just about everything else), you have to make up with items.
I would propose some changes to Morde so that he stops being a Master of None:
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Remove the W passive. Next to no one is taking Morde bot anymore, and it's a balance nightmare. This frees up some power to give back to the rest of his kit.
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Base stat buffs. Morde had his base stats nuked because he was tearing through bot lane like a starving hyena at a buffet. Since Morde isn't in bot lane anymore and his W passive can be removed to stop him from going back there, there's no harm in giving him back some defensive stats. If we remove the insignificant speed buff from W, his base MS could be safely increased to sane levels.
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Attack speed. When Q is activated it increases Morde's attack speed a set amount, then wears off when Q does similar to Taric's passive.
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Mixed damage. Q and E now do 50% magic and physical damage, like Corki. This way, no matter if Morde builds AD, AP, or both he'll almost never need pen items.
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Resists. W now gives resists to both Morde and the other target like it used to before the juggernaut changes, and they go away when the W ends or Morde pops it early. This allows Morde to focus more on building mostly HP like other juggernauts than HP and resists both. Alternatively, it can give some damage reduction instead.
With some of these changes, or all of them, Morde's kit remains versatile but also allows Morde some wiggle room with what items he needs to build. Didn't get a trinity force? Don't worry, your Q will still be quick to get to hit three. Built a lot of HP for your shield? You have resists in your kit, but use them wisely. Want to build full AD or AP? You'll still be doing mixed damage. And hey, now you might actually be able to catch someone without a rylais! Sometimes. Maybe.