You're right, some verbs are indeed used without the personal pronoun in literary contexts, but not all types of pronouns can be omitted.
Ethic datives, for example, can. Ethic datives are pronouns that emphasise the agency of the subject, its relationship with the object, a special interest in the matter, etc. They are common in conversational Spanish, but speakers tend to avoid them in more formal or literary contexts. Look how these sentences look much more formal by just omitting the pronoun (and how the meaning remains unchanged):
Me leo dos libros a la semana ⇒ Leo dos libros a la semana.
Me recorrí la plaza de arriba abajo ⇒ Recorrí la plaza de arriba abajo.
Me comí una pizza entera ⇒ Comí una pizza entera.
And now here's an example in the wild from a translation of Alice in Wonderland:
"Todo parecía haber cambiado desde que cayó en el charco"
The standard construction would have been "se cayó", but "se" is omitted to render the sentence more literary.
Indirect Objects pronouns can also be omitted to the same effect:
Dígale al señor López que pase a mi oficina ⇒ Diga al señor López que pase a mi oficina.
IOs can only be omitted when they are duplicated, and therefore they are redundant. Look how in the sentence above "le" refers to "al señor López" but both are present in the sentence, so one could argue one of them is unnecessary. For the same reason, the IO cannot be omitted if it isn't duplicated because then it wouldn't be redundant anymore:
Dígale que pase a mi oficina ⇒ Diga que pase a mi oficina (?)
The second sentence is incomplete because a non-redundant pronoun has been omitted, thus damaging the integrity of the sentence. The fact IOs are only omitted when they are redundant means there will always be something telling you what the IO is.
But what about Direct Object pronouns? Well, to be omitted they would have to be redundant (that is, duplicated) but, while IOs are almost always duplicated, DOs hardly ever are. That means they aren't generally omitted (and even when they are, that wouldn't make the sentence intransitive because you would have another element telling you what the DO is). But omitting a duplicated DO pronoun isn't as simple as with IOs. Consider the following examples (the DO is italicized and the DO pronoun is in bold letters):
(1) Las razones las conozco de sobra. (Duplicated pronoun)
(2) Mucho dinero me he gastado como para que ahora todo se vaya al garete. (Omitted pronoun)
(3) Las bebidas las compras tú. (Duplicated pronoun)
(4) Varios libros tengo que te pueden interesar. (Omitted pronoun)
The interesting thing about these sentences is that they are the only grammatically correct option. That is, all of the following are wrong:
(1) Las razones conozco de sobra. (Omitted pronoun)
(2) Mucho dinero me lo he gastado como para que ahora todo se vaya al garete. (Duplicated pronoun)
(3) Las bebidas compras tú. (Omitted pronoun)
(4) Varios libros los tengo que te pueden interesar. (Duplicated pronoun)
Now, why is it that the DO must be omitted only in certain cases but duplicated in others? I haven't been able to find any reference so all I can say is what I feel is the reason: generally, when a DO is concrete (las razones, las bebidas) it is duplicated; when it is indefinite (mucho dinero, varios libros) it isn't1. Again, this is only a feeling and may not be true for all cases, so take it with a grain of salt!
1: If course, this is only true if the DO is placed before the verb. When it's placed after it, it's always omitted except in some Rioplatense dialects.
The whole point of this (long—sorry for that!) explanation is to make evident that omitting a pronoun doesn't omit any information. If it's an ethic dative, then you didn't even need it to start with, so omitting it wouldn't change a thing. If it's an Indirect Object, then you would only omit it if it's duplicated, so again: no loss of information. If it's a Direct Object, you would only (but not always) omit it when it's duplicated, so the same thing applies. Therefore, the category of a verb (transitive or intransitive) isn't affected in any way by omitting a pronoun because the same amount of information is being provided—only expressed in a more succinct way.
In "Ella se levantaba con buena cara", the pronoun "se" is working as a reflexive pronoun. Only ethic datives, DO pronouns and IO pronouns can be omitted, but not reflexive pronouns, so "Ella levantaba con buena cara" is wrong.
In "Se despertaron temprano", the verb "despertar/despertarse" isn't easily classifiable. You can consider the pronoun "se" an ethic dative, a pronomimal verb marker or a reflexive pronoun and all of them make sense. So "Despertaron temprano" is technically correct, but it sounds unnecessarily poetic to my ear. Curiously, the similar sentence "En cuanto desperté, me acordé de ti" sounds much more natural to me, maybe because you can hear it more often. Either way, I recommend just avoiding using "despertar" without the pronoun altogether if you want to sound natural.