The schema establishes the contract between you the user and the database.
You have to help the database so that it can help you.
The information you are giving it is mostly things that it can't reliably know or decide on your behalf (such as whether you want to store 2 things together as 1 thing or not like first name last name).
The database still does a ton of stuff for your that you don't have to think about. For example SQL itself by definition is like that. You declare what you want to take out and the database figures out how to do that for you (this part is similar to the compiler optimisation of your example).
Going by your example, not having an schema is similar to saying "why do I have to write code, can't the compiler just write the code for me?".
In both cases, on one hand yes the compiler or the database does the magic for you, but at the same time it can't work without your input and decisions (writing code, or the schema).
The information you are giving it is mostly things that it can't reliably know or decide on your behalf (such as whether you want to store 2 things together as 1 thing or not like first name last name).
The database still does a ton of stuff for your that you don't have to think about. For example SQL itself by definition is like that. You declare what you want to take out and the database figures out how to do that for you (this part is similar to the compiler optimisation of your example).
Going by your example, not having an schema is similar to saying "why do I have to write code, can't the compiler just write the code for me?".
In both cases, on one hand yes the compiler or the database does the magic for you, but at the same time it can't work without your input and decisions (writing code, or the schema).