While I may be reading too much into Morena Baccarin's performance as Anna, it seems like she brings a sort of "Wait, I thought I debugged that?" confusion to scenes where people don't swallow her "I'm a friendly alien here to help" act. Where John in the original series brought a sort of blustering politician's BS to things, underlying it was a fairly human set of emotional responses. With Anna, it feels like she's running a human emotion emulator instead, leading to mild confusion and internal bugfixing when it misfires, rather than to an intensification of blathering. A brief pause where she's not quite there in the conversation before she patches her script and starts running it.
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Also, keeping the ships hovering over major cities keeps the people constantly aware of their presence, which is useful whether you're trying to be assimilated into their day-to-day paradigm OR trying to become Big Brother.