Is the personal 'I' a royal 'we'?

As an ex-Soviet for whom English is a second language, I occasionally run into linguistic constructs that I find puzzling, and I have to turn to native English-speakers for explanation.  The debate over articles of impeachment of President Trump provided a rare opportunity for schadenfreude when it became obvious that English native speakers can themselves be as confused about the meaning of an English word as I am.

In the fresh batch of debates, congressmen were debating the meaning of Trump's request of the Ukrainian president in the July 25 phone call: "I would like you to do us a favor, though."  Democrats implied that in using the word "us," Trump referred to himself with a royal "we," saying, in effect, "do me a favor and investigate the Bidens in exchange for release of the foreign aid" — thus soliciting a personal favor in exchange of the official act.  A Republican congressman, however, insisted that when read in the context of the entire sentence ("I would like you to do us a favor, though, because our country has been through a lot and Ukraine knows a lot about it"), "us" was meant to mean the U.S. — the country that went through an election-time disinformation attack followed by the divisive Mueller investigation, and that Trump's request had to do with clarifying a highly confusing question of who interfered in the 2016 U.S. election.

Perhaps because I am not a native English-speaker, I found a different aspect of that sentence confusing: if, indeed, the "us" in the middle of the sentence was used as a royal "we," how is the "I" at the start of the sentence to be understood?  The sentence, it seems to me, loses coherence: if Trump meant "us" as royal we, he had to have meant "I" that way, too.  Royal "we" would have been used consistently throughout the sentence, in which case the transcript should have read "We would like you to do us a favor, though."

Why doesn't it?

The entire legal grounds for the Trump impeachment seem to be based on grammar, on the meaning of the word "us" in the context of one sentence in the Trump-Zelensky phone call.  As one for whom English is a second language, I wonder: how does the use of an individual "I" in the same sentence with the Democrat-implied royal "we" strike the ear of a native English-speaker?  Doesn't it sound a little bit off?

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