Why are second languages taught differently from first languages?

A couple days ago I realized that first languages and second languages are not taught the same way. When learning a second language, a person is taught things such as conjugating infinitives, helping verbs, making verbs agree in number/gender with nouns, and other things. A person typically learns the use of a bunch of grammatical terms that may not even be used in a typical English class. Writing typically involves a process of applying different rules, such as conjugation, agreement, and other things.

For example, the thought process of translating “I have…” to French might be (when the language is first being learnt):
I -> Je
To have -> avoir
Conjugation of avoir with “je” is “ai”
Je ai -> J’ai
Eventually, a person will simply memorize this. However, this process represents how it is taught. When learning a person’s first language, a person can go for a long time without ever thinking about the fact that “have” and “has” are two conjugations of the infinitive “to have”.

A second example might be the formation of tenses. Early on while learning a second language, a person is taught how to form a specific tense of verb, such as “simple past”. A person might be taught the process of adding a specific helping verb and modifying the verbs in a specific way. When learning a first language, a person does not learn the various names of tenses. We hardly realize that we are using different tenses when we say “He played” vs “He has played.” We are only aware of the past/present/future aspect.

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So anyway, I want to know why foreign languages are taught differently than a first language. Are they both equally effective? Or is learning stuff such as formally of sentance structure best left until after a person already understands the language? Is total immersion, like that of learning a first language, the best way to learn a language?