Was Amaris known as having any kind of command experience?
That may, or may not matter. Just spitballin here, but...
On one hand, to claim leadership of the SLDF Amaris would have to step down as leader of the Rim Worlds Republic. The move could weaken his position at home, and among the Republican army since it might look like he's abandoning them for greener pastures. Selim was only named Regent after Amaris claimed the title of Emperor, not before.
The jump in position could also ruin all of the plans he's set into motion for usurping the Hegemony. Rather than making it easier to launch the Coup, taking control of the SLDF means operating within its boundaries, not outside of it. While Amaris might be able to continue shipping in Republican troops into the Hegemony, it might be more difficult.
Plus, moving to the SLDF is not a lateral move, it's actually a step down and away from the throne: literally. Amaris would have to take command of the SLDF, this means leaving Terra and the Hegemony for the front line. This could seriously threaten or stall plans for the Coup.
Also, while Richard II may or may not have the juice to appoint Amaris as Commanding General, his lack of military experience will likely stipulate titular control while he becomes "acclimated" with command and the SLDF. (Actually, I can almost guarantee it should Amaris make it past the High Council.)
So as Commanding General, Amaris might be closely scrutinized by a truly loyal member of the SLDF, or worse, forced to go through "SLDF boot camp" to learn the skills he needs to lead. Either way, his ability to direct the SLDF is affected, so taking command of the SLDF might actually hurt his powers, not expand them.