I totally agree with your conclusions which is why I put in special conditions that his orders would appear to come from the Emperor directly to get round this. I think the advantage to this is that there would be no jealousy issue either as no-one would know that Alpharius/Omegon were actually Warmaster as the other Primarchs would think their orders were coming from the Emperor directly. Exactly the sneakiness we'd expect from A/O as well
If the orders appear to be coming from the Emperor, Alpharius isn't a Warmaster. Not having an official Warmaster defeats most of the point of having a Warmaster, which was that the Emperor could retire to his webway project without being bothered. If people think the Emperor's still in charge then they're going to keep trying to get in touch with him. Maybe the Alpha Legion can head of most of those attempts but remember that the Warmaster doesn't just command the Astartes but the entire military might of the Imperium, like Mars. Mars is very close to Terra, you don't think Kelbor-Hal might try to get in touch with the Emperor directly? Or what about Magnus, he can talk to the Emperor directly across space. How is the Alpa Legion going to intercept that? All in all the Alpha Legion would be so busy faking the Emperor's continued presence that they'd be quickly found out when there ability to campaign disappeared.
Night Haunter - "I think it's a stupid rumour but I'm happy that my Legion is no longer criticized for using it's preferred tactics.
For the record: the Night Haunter and the Night Lords were never official criticized, sanctioned or otherwise punished for their behaviour. At no point did the Emperor show anything but approval for their actions.
I think Alpharius/Omegon would be brilliant at exploiting the other Primarchs and Legions to their best effect by having Alpha Legion marines within the other Legions to find out what they want, whether they're happy or annoyed and then taking measures to keep them happy.
Alpharius is a smart guy (though other Primarchs are just as smart) but he's never really shown himself to be a psychological manipulator of any real skill. Many of his brothers true motives are hidden even from themselves until they are exploited in their fall. You are expecting Alpharius to know more about his brothers (who he's only know for a couple decades and even then not personally) than the Emperor knew about his sons (who he crafted for the gene up).
The view we get of them in Legion and then in Deliverance Lost really impressed me with how effective the Alpha Legion are at infiltrating the other Legions
I highly doubt that the Alpha Legion possesses the ability to infiltrate agents into all the other Legions, let alone get those agents into a position to be able to determine the psyche of their Primarchs. Remember that the infiltration of the Raven Guard took place in the complete chaos of Istvaan, an unprecedented opportunity. Other Legions have numerous language, behaviour and cultural quirks that would make them more difficult to infiltrate. And also remember that one of the Alpha Legion operatives comes very close to blowing his cover in the Raven Guard.
And of course you're assuming the Emperor would be okay with the Alpha Legion infiltrating all the other Legions (and non-Legion military bodies). And why would he be?