In the accepted answer to: The difference between an analogy and a metaphor? an insightful conclusion was reached that the analogy is what is expressed and the metaphor/simile are how it is expressed. I think for most cases this is a perfect rule of thumb.
For the purposes of this post, I want to pose the question, that under very specific circumstances we can have an analogy itself only. In other words, an analogy without a metaphor or a simile. This may need certain assumptions about the clarity of the analogy. Take this analogy for example:
You cannot have a rainbow without rain, and you cannot have success without hard work.
The above example doesn't fit as a simile. I'm not sure if its fair to consider it a metaphor either, it doesn't seem to fit the spirit of most metaphors I've seen: "speak daggers", "time is money" … While "rainbow" and "success" are being compared, it lacks the figurative dimension, and so, to me at least, it seems to be a stretch to call it a metaphor. Maybe it's simply a comparison.
Question: What is the best classification for my above example? Is it conventional to argue an analogy can be expressed on its own, as I have speculated? Or does this example fall into the category of metaphor after all?
Another noteworthy example:
Time travel felt as if I was in a runaway carriage.
Edit I just noticed there was an "as" in that line. It could be substituted with "similar to" to escape the simile jurisdiction.
A better one yet:
Imposing a tarrif won't address the root problem of why we have such a big trade deficit, by the same logic: putting a bandage over a skin cancer growth won't change your prognosis.
No obvious simile hallmarks: "like" or "as" (maybe like/as are not mandated for similes?) Also, doesn't strike me as a metaphor. It seems like analogy is the best term for it, but maybe that's just me.