> That, along with competition (if applicable, see below), drives them towards minimizing costs, increasing efficiency, and innovating.
Highly debatable. Not making a profit on paper (or moving it to low tax-environments) is a great way to dodge paying taxes. Innovation is a side effect of competition, not of profit-seeking. Plenty of examples of oligopolies and monopolies where innovation ground to a halt in favor of siloization, buying up competitors, dark patterns, regulatory capture, etc.
The right way too look at this is that the organisation of private industry creates a selection pressure on "making money" (not profit!), with the minimum being "able to cover costs" and thus stimulates evolution of strategies to do so. Like in biological evolution, there are many, many pathological situations that can occur.
> Government has the major focus of taking money, and largely spending it arbitrarily.
This is false. The US is a bad example because it has an incredibly corrupt political system, especially since Citizens United. In general in most modern developed democracies spending by the government is supported democratically to a very large extent. That is not to say that 80% of citizens support each bit of spending, but for 95% of the things where money is spent by the government, a majority agrees that money needs to be spent there. The word "arbitrarily" is definitely not warranted.
> would you characterize Amazon as bloated, corrupt, and inefficient, despite being an effective monopoly?
Don't know, yes, and don't know.
For corruption, I think it is necessary to determine how it would even look like for Amazon. Corruption in government is often "favoring entities friendly to the people making the decisions over objectively better options". I'd argue that that is wholly accepted in private enterprises and even encouraged. A "quid pro quo" in private enterprise is just "a business deal" or "customer relations". "Nepotism" is just "helping your friends out". Etc.
I would assume that things like that are very, very common within Amazon.
With regard to bloated/inefficient: This is incredibly hard to make definitive statements on without having worked there and having a lot of intimate knowledge, so I'll refrain from doing so. I think it is, but I don't know.