This is actually quite an interesting topic and opens up a whole can of worms regarding how to think about Japanese grammar. I will try to give an overview without going too far down an irrelevant sidepath.
There is a general argument within Japanese linguistics and amongst grammarians over how to actually describe Japanese grammar. One complaint that has come up at various points in various areas since the post-war period is that Western linguistics and grammar has been applied to Japanese where it really doesn’t fit. This argument is still ongoing to this day and can get rather complicated. One point of contention in this argument is that the idea of transitive and intransitive verbs (他動詞と自動詞) is not suitable for Japanese. There are various reasons to be for or against this. One clear reason is that the particle which indicates the direct object (or the accusative case, if we speak in terms of cases) doesn’t consistently behave in the way you’d expect such a marker to act. The question you have raised, about psychological/emotional verbs using を, is exactly one such example.
In Japanese dictionaries these kinds of verbs are not reliably listed as being transitive or intransitive between different publishers. Sometimes they’re listed as being both, which is really quite rare for Japanese verbs. For example, 喜ぶ has the corresponding transitive twin 喜ばす which is arguably just a form of the causative 喜ばせる. You’ll notice that the direct object of 喜ばす is whoever is being made delighted, which is much the same as used “to delight” transitively in English (He delighted the audience). So then are both 喜ぶ and 喜ばす transitive despite somehow having completely different sorts of things marked by を? What even leads a publisher to choose whether to list a verb as transitive or not? If it is sometimes used with nouns marked by を does that make it transitive? This is the crux of the issue and a debate even amongst the experts writing dictionaries.
Let’s assume you want to say that both are transitive, 喜ばす quite uncontroversially and then 喜ぶ being perhaps more borderline but it takes a noun marked with を so that seems good enough for labelling purposes. However this argument seems to fall down when we are confronted with another use of を which foreign speakers can struggle with, being with movement verbs such as 歩く. 歩く is pretty much uncontestedly intransitive yet it is also used in patterns such as 公園を歩く(To walk in/around/about the park). So probably just the fact that を can be used with a verb is not enough to make it transitive.
Looking back at the psychological/emotional verbs, as you have noticed the thing marked by を is also not what we would imagine to be a direct object (neither is the park in the above example). In fact, the thing marked by を is the cause or source of the emotion and not something being acted upon by the verb. There really isn’t a way to cleanly put this into English without fundamentally changing the grammar/structure. The flipside of this is that the grammatical analysis (based on Indo-European grammatical ideas) then doesn’t seem to make any sense. This is what I think @drunkgome was getting at - perhaps you have been a little unfairly abrasive in response.
So to answer this:
The simple answer is just this is how it works in Japanese and the point of confusion is arguably that the majority of grammatical models of Japanese struggle account for this kind of usage.
If you would like to maintain を as something that only indicates what might be normally understood as a direct object when used with psychological/emotional verbs then Wiktionary uses this definition:
感情を伴う行為の対象であることを表す。
Meaning, you could still consider these verbs to be actions of some sort and somehow the cause of these actions is the direct object of them.
For further reading, the Dictionary of Japanese Grammar has an entry on this usage of を and you can find various discussions about it online if you search in Japanese. There are more reasons to be suspicious about the traditional analysis of を which I have not gone into (usage with certain adjectives and aux words, (non-)usage with できる, usage with てある, etc).
Something that may or may not help: You brought up “thinking” as something where you could perhaps see how the subject of a thought is like a direct object. If you consider the difference between と思う and を思う you can see that を思う lends itself more to being translated as thinking about something. It may also be useful to consider this in relation to psychological/emotional verbs. E.g., 〇〇を喜ぶ —> To be delighted about 〇〇. Comparing this with △△と喜ぶ may further highlight the differences, wherein と does not indicate the subject of a thought/feeling so much as the way in which one thinks/feels.
