Note that, while Arkhan does suffer more than the other mortarchs from the rules of one and summoning restrictions, he also costs less - fully 100 points less than neferata, and 120 points less than mannfred.
And while Mannfred's command ability is better than Arkhans, no argument there, IMO it isn't good enough to give up on the new command traits, so you're still better off taking another character as your general, at which point neither of their command abilities mean anything at all, and arkhan's points discount means all the more since you can use those spare points to buy a generic hero to be your general - Arkhan plus a wight king with black axe comes out to exactly the same cost as mannfred, for instance.
Even with all that, Mannfred's superior melee abilities and only-slightly-inferior casting (he gets casting bonuses, even if they're not as big, and his signature spell is considerably better) mean that he's the better all round choice - though, again, you'll still want to pick up a back up hero to do the busywork of actually commanding the army while Manfred soars above doing his own thing.
The exception is if your army gives casters extra things to do. Summoning is much weaker now, but is still a thing. A surprise appearance of 20 skeleton archers can do remarkable things, especially if you have a wight king commander nearby to buff their number of shots. Even more than summoning, many Death units in the tomb kings compendium come with healing spells. Necropolis Knights, Sepulchral Stalkers, Sphinxes of all sorts (including Necrosphinxes), Tomb Scorpions, Ushabti, Bone Giants (not a heal, but a buff) all give Arkhan the chance to really flex those casting bonuses, and in an army featuring a few of these units you'll hardly care about rules of one or summoning restrictions.
And a Royal Warsphinx in particular gives Arkhan an extra healing target that doubles as a particularly intimidating and surprisingly difficult to remove generic general, thanks to its large number of wounds, wound-halving mechanic, healing spell, reasonably intimidating melee attacks, and solid command ability (in deathrattle heavy armies). Take him with 'Ruler of the Night' to give your army, including Arkhan and the Royal Sphinx, 5+ FNP saves for extra durability. Or take him with red thirst, doubling his melee output.
You can take the same hero with Mannfred, but mannfred's extra 120 points cost over arkhan will really start to hurt when running two behemoth leaders, particularly when the royal warsphinx wants you to run more deathrattle units rather than just shrugging the battleline tax off with some zombies, and arkhan will be noticeably better at healing the sphinx lord.
So yeah, for the most part, if you're looking for an all-round mortarch that can fit into most armies, and in particular if you want a mortarch to be your general (though giving up command traits makes that an iffy prospect regardless), Mannfred - or Neferata - are the clearly superior choices.
But within the context of particular armies that have extra use for potent casters AND already have other large heavy hitters eating up much of their points, Arkhan definitely has a place. And honestly, it's not entirely unfitting that Arkhan proves to be a more attractive mortarch in more Nehekharan-leaning undead armies.