One ring adds to Whirling Death, the other adds to Execution. He wields a two handed scythe and wouldn’t benefit from his own rings. I was thinking that instead of adding to those skills they could enhance Spectral Strike from his MI weapon and the other one could enhance Deathchill and/or Glacier.
Or you could just let him drop a t-shirt that reads “I signed up for endless torment and all I got was these lousy rings”, implying that he got screwed over. Problem solved. 
As long as we’re on this subject I would like to file a complaint about Benn’Jahr’s pauldrons. It is clear to see that he wears no pauldrons. He couldn’t even use proper pauldrons, he is too big. And why is Iron Maiden not actually made out of iron? This is a terrible oversight.
Item Skills can’t benefit from +skills.
No, but they can be augmented in other ways. The expansion has brought us uniques like Mythical Crimson Spike that converts the Piercing Damage of Ring of Steel to Vitality Damage and adds 2% Health Restored to Wendigo Totem. I don’t see how my suggestion is out of the realm of possibility.
Except the skill modifiers only affect mastery skills. None of the skills you mentioned are from masteries.
On a more serious note, it is many times the case that a piece of BiS gear for any given build will contain skill boni that never get used, PARTICULARLY after the AoM release. Alkamos would still benefit from most of the other stuff on the rings besides the +skills. Besides, maybe Alkamos preferred dual wielding when he was still alive.
So far, yes.
None of the skills you mentioned are from masteries.
Do they need to be? I’m just thinking outside of the box here to make some set items make a little more sense.
Krieg isn’t a necromancer but drops a weapon that improves Raise Skeleton. It’s just how these items work, so they are useful for more then just one build.
He drops a Monster Infrequent that has a chance to improve raise skeleton. I’m not talking about Monster Infrequents, which can vary in their abilities. I’m talking about a set with a specific theme. I’m suggesting a way to improve that theme. The blow back and weird pedantry in the comments is weird to me. I guess if we’re being pedantic here you could make a case for Raise Skeleton being available on one of his Monster Infrequents means that he is indeed a Necromancer and the undead that spawns at the beginning of his room is was a way to show that before the expansion introduced the class. But I’m not being pedantic. I’m just trying to make a suggestion that makes sense to me. That’s what this forum is for.
And his armor set has bonuses for soldiers and arcanists. The rings and the scythe are not an item set and therefore their use should not depend on each other, they are seperate. The game is made so that builds can be flexible and not every item dependant on another item. Some high level sets and items even have bonuses to skills from 3 masteries to be more flexible. That’s all I meant.
I’m pretty sure they need to be. Also, a lot of dual wielding builds have been made with these rings (Spellbreakers being the most popular) and your suggestion would piss off a lot of people because of the loss of pluses to dual wield wps skills.
A level 94 set giving skill modifiers to leve 25 and 35 relics makes no sense. Mainly because nobody is gonna use these at the same time when Nightblade has Nemesis relic. Last, nobody uses Alkamos green MI when he has Soulrend which is far better.
Are you speaking with knowledge of how the game is coded or just making a guess?
Also, a lot of dual wielding builds have been made with these rings (Spellbreakers being the most popular) and your suggestion would piss off a lot of people because of the loss of pluses to dual wield wps skills.
This is a fair point, but even I’ve been burned by item and skill changes in the past. I’m the kind of guy that would be mad about it for like a day, and then change my build and move on.
A level 94 set giving skill modifiers to leve 25 and 35 relics makes no sense.
Another fair point, but there is more than one tier of the Alkamos set and more than one tier of Relic with the same basic themes. Adjust accordingly.
Mainly because nobody is gonna use these at the same time when Nightblade has Nemesis relic.
This is a nice relic but there is more than one relic in the game that is useful for nightblades.
Last, nobody uses Alkamos green MI when he has Soulrend which is far better.
Soulrend doesn’t have Spectral Strike. It’s a nice Legendary but in the build I’m using, I’d probably keep using Alkamos’ MI instead. The point I’m trying to make here is ‘nobody’ is the wrong word to use. While BIS weapons are nice to have if it was the only option for every build, this wouldn’t be a very good game.
I’m pretty sure skill modifiers only affecting masteries is for consistency because allowing them to affect outside items would be more trouble than it’s worth (Even more balancing required).
This set has been like this for well over a year and Crate made it this way fully aware that Alkamos only wields two handed weapons. If they wanted the set to support Alkamos stuff they would have, but they didn’t.
And remember that the scythe specifically isn’t part of the set.
Maybe his build was just all over the place. 
But yeah, I like the rings as they are and there’s already SS gear out there but cold default attack is actually pretty hard to itemize, losing these rings too would make it even worse.