No, bureaucracy also includes elements of social dominance by people who have no other means to assert status (or sometimes outright covert sadism), busywork, and processes that are rule-based - often dumbed down in the hope that people with limited intelligence don't make avoidable mistakes - rather than responsive and reality-based.
Getting agents to deal with their own versions of these issues is an interesting experiment.
I personally find that to be a bit of an inversion. People will utilize leverage and identity in whatever context, so mixing that in doesn't seem cogent to me.
But maybe the two are genuinely tied together enough that it's deserving to be a part of the definition, I don't know. Tried looking up the definition, I'm not really convinced.
For the longest time I considered the "hate on bureaucracy" more of a reactionary trope rather than anything actually coherent. Maybe this is just another one of my cultural differences of many. It's not as if people forming consensus, keeping count, or delegating authority were ever actually possible (or desirable) to escape, comes with scale. So to try and paint it as some odd devilish plague always came across to me as dilettante, though maybe it's more me who's simply never grasped the whole dynamic and the cultural position around this fully.