Perhaps I'm misunderstanding, but are you using some much more restrictive definition of 'metaphor'?
For example, as far as I can see, one can't escape metaphor because they're deeply embedded in the very language you're using right now.
The most basic metaphors are ones that refer to the body or the physical world. Jar [1] originally refers to a 'screeching sound'. Understand probably from the literal sense to 'stand between' [2]. Compute derives from 'com' (together) + 'putare' (reckon, settle an account) [3]; the latter root originally comes from Indo-European 'to prune'. Almost all vocabulary is in fact a form of extended metaphor; in fact, it cannot be any other way, because to describe a new thing requires one to compare and contrast it to existing things.
You yourself are making a metaphor when you say that an analogy has to 'at least rhyme' — a metaphor for poetic sound similarity to stand for a sort of logical similarity.
The distinction between an analogy, where one explicitly calls out the comparison ('like', 'as'), and a metaphor, where the relationship is taken implicitly, is much blurrier than it seems. All our language and thinking is saturated with metaphors at every single level, to the point where they seem to be taken for granted and disappear.
IMO, the problem is not metaphors themselves, which are unavoidable; it's picking wrong metaphors (which is really using the wrong language) that lead us astray.
[1] https://www.etymonline.com/word/jar
An analogy, or analog, is a much deeper match in that means to transfer the understanding and knowledge of an existing system to a new target system that closely parallels that understanding and knowledge. Analog computing was literally "creating a model of the problem" that closely matched the real problem.
Agreed that metaphors are not inherently bad, but the dependence on metaphors rather than analogies is symptomatic of a lack of depth in understanding when attempting to convey knowledge.
From reading the book, if someone says that "In a complex world we perceive, think, understand and communicate metaphorically.", I get what they mean. It occurs to me that her use of the word "metaphor" follows from such a comprehension.
Are the metaphors actual tools, or more like metaphorical tools?
e.g. the desktop metaphor
There is a reason that analog computing mattered, and why no one seriously focuses on metaphoric computing (except, you know, as a metaphor for something that isn't computing). I suspect that metaphors are the tools of cargo cults while analogies are the tools used by those that actually understand a system in order to convey it to those that do not.