Let’s evaluate naturalness in polite style first because plain style hides some of the unnaturalness.
Suppose you are discussing with someone which restaurant to choose for your next gathering. Taro is absent but he will also be at the gathering. You decide to convey his preference to another person.
You would probably say either one of the following.
Taro may or may not have directly told you that he wants to eat spicy food for this particular occasion, but he was certainly giving off that impression last time you spoke to him about the matter. If this information turns out to be incorrect and he later tells you that he didn’t want to eat spicy food, you would probably argue with him, pointing to the earlier behavior or words of his that made you assume he wanted to eat spicy food.
You may or may not have heard this from Taro or someone else, but you somehow got the impression that Taro wants to eat spicy food. If this information turns out to be incorrect, you would probably have to accept the blame because it was your judgment, after all. #3 sounds more formal than #2.
This is hearsay. (Note the い before そう.) You have certainly heard this from Taro or someone else. If the information turns out to be incorrect, you would probably blame the source while feeling somewhat responsible for conveying incorrect information without verifying it.
This is similar to #4, but you are rather indifferent to the accuracy of the information. If it turns out to be incorrect, you don't have a clear source to blame and you definitely don’t want to take the responsibility yourself.
Now, suppose the discussion is going the other direction, and you decide to remind them that Taro wants to eat spicy food by reiterating it. You might say:
In all these sentences, 食べたい is used in a subordinate clause with an expression that conveys some mood. I for one cannot think of a realistic context where the following straight assertion truly sounds natural.
It only sounds natural in a rather artificial context where you are describing Taro with complete objectivity like a voice-over narrator in a documentary video.
Now, back to plain style. If 太郎は辛いものを食べたい sounds natural in some contexts, I would say it is because it works as a substitute for at least some of the more complete sentences above.
On the other hand, the following is a natural statement about Taro’s, more permanent, preference.
If Taro has declared that he likes spicy food, it is fact enough for you. You don’t need to assume anything.