Could unwholesome craving cause the wholesome desire for enlightenment?

Why would one have desire fo enlightenment? Well, to end suffering. Why would one have desire for suffering? If you don't feel like ending your suffering, maybe you're not aware engough to pursue Buddhist path. Stick to philosphy and religion.

Based on theoriginal question:

Householder,

Aside that craving (tanha), lit. thirst, does not really differ in meaning to desire, will, cetana..., it is not necessary unskilfull, but required all along the path => refined becoming (bhava), and becoming, caused by tanha, is also the prerequisite for being able to develop the path:

"Fabrications have ignorance as their prerequisite, consciousness has fabrications as its prerequisite, name-&-form has consciousness as their prerequisite, the six sense media have name-&-form as their prerequisite, contact has the six sense media as its prerequisite, feeling has contact as its prerequisite, craving has feeling as its prerequisite, clinging has craving as its prerequisite, becoming has clinging as its prerequisite, birth has becoming as its prerequisite, stress & suffering have birth as their prerequisite, conviction has stress & suffering as its prerequisite, joy has conviction as its prerequisite, rapture has joy as its prerequisite, serenity has rapture as its prerequisite, pleasure has serenity as its prerequisite, concentration has pleasure as its prerequisite, knowledge & vision of things as they actually are present has concentration as its prerequisite, disenchantment has knowledge & vision of things as they actually are present as its prerequisite, dispassion has disenchantment as its prerequisite, release has dispassion as its prerequisite, knowledge of ending has release as its prerequisite." (Prerequisites)

For whom?

the ending of the effluents is for one who knows & sees, I tell you, not for one who does not know & does not see. For one who knows what & sees what is there the ending of effluents? Prerequisites

One may look out for "The Four Right Exertions", in The Wings to Awakening

Perhaps the most surprising element in right exertion is the role played by desire, which is usually associated with the craving that acts as a cause of suffering. We will treat this topic in more detail under the bases for success [II/D], and simply note here that the Buddha recognized that desire can be either skillful or unskillful, and that he freely admitted that skillful desire is a necessary factor in the path to the end of suffering and stress...

Whats the problem with the use of the word craving, tanha?

The Buddha used this world, for the most, as craving after the world, the six senses:

And what is craving? These six are classes of craving: craving for forms, craving for sounds, craving for smells, craving for tastes, craving for tactile sensations, craving for ideas. This is called craving.

Now think, better look with proper attention, of what you are actually g/crave for?

So when ever reading tanha, keep in mind that it is not thirst per-se, but desires in the world that distracts one from developing thirst after beyond.

(Note that this gift of Dhamma is not dedicated for trade, exchange, stacks or entertainment but as a means to make merits toward release from this wheel)

Why would one have the desire for enlightenment?

In my experience it's something like:

1. Craving
2. Suffering
3. Want to satisfy craving to end suffering -- but craving is unsatisfiable -- so is there an alternative?

Then it's suggested that that there's not only a solution for this problem but for all problems i.e. "enlightenment".

After which I guess that ("enlightenment") might for some people become a new, shiny, object-of-craving.

I guess that (i.e. "enlightenment as an object of craving") also happens when enlightenment is valued in society like money or status or power -- instead of "I'm richer than you" or "I'm better born then you" it's "I'm more enlightened than you".

You wrote ...

From this question, we see answers stating that one has the wholesome desire for enlightenment, and not craving for enlightenment

... but I don't think that's quite right: instead I guess that people can even have an (unskilful) "craving" for (imaginary) "enlightenment" -- what that question was saying was only that some desires are wholesome.

This answer for example suggested that "craving" is an split between what's wanted and what is. I suppose that wholesome desire is, by contrast:

• Wanting something wholesome
• Skilfully acting to reduce or zero the distance between what's wanted and want is

Could unwholesome craving cause the wholesome desire for enlightenment?

Things have several causes. I suppose that craving might cause a need for liberation (i.e. cause dukkha and a state in which cessation of dukkha is desirable), but it's because of right view (rather than craving) that unwholesome craving becomes wholesome desire.

Having craving for enlightenment leads to extreme effort that balanced effort. This can also lead to extreme ascetic practices. Craving for enlightenment is craving for non-existence (Nirvana), becoming enlightenment being an or some form of some Brahmic or divine existence.

Being motivated to achieve enlightenment does not lead to extremities. This is not excessive desire (Tanha) but intention or motivation (Chanda). If developed this way it becomes an Irddipada.

The distinction makes here is the desire to become or desire to act without too much attachment to the result. If your desire is to become your goal is bigger than the path and you might justify any path which you might think will take you there. This can be the wrong path or even excessive effort. If you are limited to taking action, without excessive desire for the end result, then you will take balanced steps on the right path.