However, why teach が instead of けれども, which is also quite formal? Is it because けれども is more of a spoken word? – charlieshades 5 hours ago
Ga plays such a huge role in grammar and creating the direction and feel of a sentence. Ga carries more meanings than "but" as shared with けれども and the ability to distinguish that is key understanding a sentence.
The book I mentioned on the original post offers over 10 ways GA becomes different in meaning in English.
Learn the base, then the manipulation. for example, you learn けど/けれど first then a unit comes up saying "oh you can also use が in this case....but が also means this, this, this, this and this...oh and this.
Or learn が then learn けれど can replace this one usage of が.. – Mark 3 hours ago