Why are desires in The Five Hindrances only about "sensual" desires?

Chanda = will; aspiration, being interest.

Kāmacchanda = akusala-chanda = will+sensual desires, aspiration of sensual desires. interest and attaching, needing.

Kusala-chanda = will+wholesome mind and mind factors, aspiration of wholesome mind and mind factors. Being interest but not attaching, ready for giving.

You can found them in AN 10.51, PTS: A v 92, Sacitta Sutta:

{51.1} Sace bhikkhave bhikkhu paccavekkhamāno evaṃ jānāti abhijjhālu bahulaṃ (=kāmacchandho) viharāmi byāpannacitto bahulaṃ viharāmi thīnamiddhapariyuṭṭhito bahulaṃ viharāmi uddhato bahulaṃ viharāmi vicikiccho bahulaṃ viharāmi kodhano bahulaṃ viharāmi saṅkiliṭṭhacitto bahulaṃ viharāmi sāraddhakāyo bahulaṃ viharāmi kusīto bahulaṃ viharāmi asamāhito bahulaṃ viharāmīti tena bhikkhave bhikkhunā tesaṃyeva pāpakānaṃ akusalānaṃ dhammānaṃ pahānāya adhimatto chando (=kusala-chanda) ca vāyāmo ca ussāho ca ussoḷhi ca appaṭivānī ca sati ca sampajaññañca karaṇīyaṃ

When reflecting if the bhikkhu knows, for most of the time I abide coveting (=abhijjhālu=kāmacchanda), abide with an angry mind, abide with sloth and torpor, abide restlessly worrying, abide with doubts, abide with hatred, abide with a defiled mind, abide with a violent angry body, abide lazy and distracted, he should arouse a lot of desireinterest (=kusala-chanda), effort, zeal, unhindered action and mindful awareness to dispel those demeritorious things.

Note: In this sutta, buddha used 'abhijjhālu' word instead of 'kāmacchanda' word to avoid the confusion between kusala-chanda (kāmacchanda) and akusala-chanda (chando in above sutta). It likes an avoiding confusion between made-known-viññāṇa (object) and knowing-viññāṇa (subject), when buddha used 'viññāṇa' word as object (focused point) of the practitioner, 'citta' word as the practitioner (focusing doer/undoer;subject) in anattalakkhaṇasutta.

In path of purification:

chanda:

150. (xxviii) Zeal (desire) is a term for desire interest to act. So that zeal has the characteristic of desire interest to act. Its function is searching for an object. It is manifested as want for an object. That same [object] is its proximate cause. It should be regarded as the extending of the mental hand in the apprehending of an object.

kāmacchanda:

162. Of these, greed has the characteristic of grasping an object, like birdlime (lit. “monkey lime”). Its function is sticking, like meat put in a hot pan. It is manifested as not giving up, like the dye of lamp-black. Its proximate cause is seeing enjoyment in things that lead to bondage. Swelling with the current of craving, it should be regarded as taking [beings] with it to states of loss, as a swift-flowing river does to the great ocean.

kusala-chanda:

143. (xiii)–(xv) By its means they are not greedy (na lubbhanti), or it itself is not greedy, or it is just the mere not being greedy (alubbhana), thus it is non-greed (alobha). The same method applies to non-hate (adosa) and non-delusion (amoha) [na dussanti, adussana = adosa, and na muyhanti, amuyhana = amoha (see §§171,161)]. Of these, non-greed has the characteristic of the mind’s lack of desire for an object, or it has the characteristic of non-adherence, like a water drop on a lotus leaf. Its function is not to lay hold, like a liberated bhikkhu. It is manifested as a state of not treating as a shelter, like that of a man who has fallen into filth.

You can also see the abhidhammatthasaṅgaha for more information and relativity of chanda compare with lobha (kāmacchanda).

The five hindrances is a teaching for meditators &, originally, obviously primarily for monks. Therefore, the worldly desires mentioned are generally not relevant to the life of a monk. The point of sensual desire is, obviously, it is a biologically based desire (in relation to sex & food) that is difficult to extinguish.

As for some of the other examples in the question, such as "I should have done otherwise", "why did she say so to me", "I need to find a solution", "I must improve", these appear to be examples of the hindrance of restlessness & remorse. "Why did she say so to me" could also be ill-will.

Perhaps desires for "things" are ultimately sensual ... including power, social status, physical security ... because how could you desire these things if you were unable to sense them?

But some desires might not be considered unwholesome, a hindrance: wanting to improve, wanting to find liberation, etc., may be considered skillful. Thoughts like these may be quieted eventually but I'm not sure they're a hindrance (or not necessarily and unambiguously a hindrance) as such.

Some desires (i.e. chanda as opposed to tanha) are seen as wholesome and even necessary.

It seems that the five hindrances are obstacles to the five factors to be developed in the first jhana. There are other hindrances but these five are important in the context of progress in meditation.

According to Access To Insight:

Buddhaghosa states that the abandonment of the five hindrances alone is mentioned in connection with jhana because the hindrances are the direct enemies of the five jhana factors, which the latter must eliminate and abolish. To support his point the commentator cites a passage demonstrating a one-to-one correspondence between the jhana factors and the hindrances: one-pointedness is opposed to sensual desire, rapture to ill will, applied thought to sloth and torpor, happiness to restlessness and worry, and sustained thought to doubt (Vism. 141; PP.147). Thus each jhana factor is seen as having the specific task of eliminating a particular obstruction to the jhana and to correlate these obstructions with the five jhana factors they are collected into a scheme of five hindrances.

The Jhanas in Theravada Buddhist Meditation https://www.accesstoinsight.org/lib/authors/gunaratana/wheel351.html#ch1

Meditation teacher Gil Fronsdal comments here on why this hindrance is focused on sensual desires rather than other desires:

Perhaps sensual desire is singled out as particularly hazardous to meditators because reaching for pleasure and avoiding pain are more basic than other desires. Even when the mind is still enough not to be caught up in other desires, the enticement of pleasure can still be operating. When the grip of sensual desire is strong, it often pulls us into the world of fantasy and imagination. Sometimes it is the pleasure of fantasizing itself that holds us more than the object of our wants.

While there is nothing inherently wrong with sensual pleasure, the desire for it is called a hindrance when it interferes with our ability to stay present. During meditation, even the most innocent desire can distract awareness from the razor’s edge of the present moment. If we want to stay on that edge, we need to let go of anything that causes us to slip off it.

Obsession with more complex desires would fall under the hindrance of restlessness and worry:

Frustrated desire and pent-up aversion are common causes of agitation. Fear and resentment are others. Dissatisfaction is a cause that can keep the mind restless with searching. Trying too hard in meditation can also stir up the mind. When any of these are primary, it can be more useful to be mindful of them than the restlessness. Ignoring the causes can keep us skimming the surface; being mindful of the underlying causes can help with the settling.