You cut off the parens which said the “love” was first person singular version of the verb. I was showing that in Latin the subject is often within the verb, so that while we would normally translate “te amo” as “I love you” there is actually no “I” in that sentence, it is simply understood that since “amo” is the first person singular version of “amare” (to love) that it is “I” doing the loving without any need to put “ego” in the sentence. Also seen in another famous sentence “cogito ergo sum”, when we tranlate it into English we include two “I”s that aren’t actually in the sentence, merely understood because of the conjugations. Conjugation is a powerful tool in language and the Romans really used it to their advantage, they let it streamline the language and also give them a tool for added emphasis.
Then I missed your point. I agree that implicit conjugations like those you describe are handy linguistic shortcuts. Spanish is very similar. You can add the pronoun if you choose, but it’s generally not necessary.