I learned to design websites without the use of Frameworks back in the day; but as I learned more, and did more sites; I ended up having a respository of classes that I would need; and essential classes, that made my life as a coder easier. I then tried cakePHP and other frameworks, figuring out that; throught out my years of programing, i ended up creating my own personal framework that hasn't failed me yet
Frameworks make coding somewhat a little faster for the traditional coder, and can prove to be quite efficient.
For example I am currently working on a site that is built of a Moodle Build. Within their framework they have the function get_records($table, $searchfield, $serachvalue, [$limit]);
which takes care of querying the database, returning the value, and then run a foreach on all the rows, and returns them into an object.
Its saves me ton of time and I dont have to repeat the same code over and over again.