I don’t think there is a blanket statement that you should only ever use a single primary key named id.
Most people use a surrogate primary key as an auto generate int, because it isolates the primary key from ever needing to be changed, like if you make the PK the user name and they later changed their legal name. You would have to update the PK and all FK columns to reflect the new name. if you had used a surrogate primary key, you just update the user’s name in one spot (because the tables join on the int not the name).
The size of a primary key is important because the PK is duplicated into every index you build on the table. If the PK is large (like a string) you have fewer keys per page in the index and the index will take more cache memory to store it. Ints are small.
Having a auto increment int PK lends itself to being a clustered index well, as rows are stored in this order and there is no need to go back and bump rows out of the way to insert a new row, you always add to the table’s end.