Nothing about socialism requires a handful of people to control everything.
Anarchosocialism, very popular these days, considers deep hierarchical systems to be intrinsically broken and unfixable. The money quote here would be, "Power flows up from below". While there is still a need for organization at a high level in such a system, these people should be coordinators only with no ability to set policy.
Many anarchosocialists are also in favor of sortition - where the coordinators are randomly chosen from the eligible population by a fair lottery.
Who knows if this would work? It definitely has the emotional appeal for me, though.
My feeling is that the real problem comes from about 4% of the world's population that are sociopaths and this system goes a long way to preventing these people from gaining power as well as mitigating the damage when they do: 4% sociopaths in positions of responsibility is a lot better than today's 90%.