Likewise, when a musician sees a run of adjacent notes without accidentals, they immediately know what to play. They don't need to inspect each one in turn to determine how many semitones it lies from the previous note. Likewise, when a composer wants to write such a run, they can just draw some black dots in a row. They don't need to squint at a grid and select the correct rows each time.
To sum up, traditional notation is uses a form of compression that makes reading and writing diatonic music easier.
Taking this even farther, some systems of music notation compress things even further and don't explicitly list all of the notes to be played. For example: figured bass, basso continuo, or even just chords that accompany lyrics. In fact, even regular sheet music doesn't usually precisely represent of duration of all of the notes. Some notes are sustained and bleed into others, some are meant to be played strictly in time. Human interpretation is an important part of the process.
On the other hand, the piano roll is a MIDI editor. It is a great way to tell a computer exactly what to play, but it is not easy to read quickly and it is impractical to print or write by hand. Both forms of notation have advantages and disadvantages but it seems to me you haven't spent enough time with the standard notation to fully appreciate its advantages. In other words, the piano roll notation might be your blub language for music. [1]
Because the most important thing is the actual semitone intervals, and the standard notation hides them and gives them weird names like augmented fourth (it's just six semitones, just call it that). And it names the 12 semitones based on the c major mode even though that's only one of about 50 modes/scales/keys you might want to use.
Similarly, key changes are explicit in sheet music but hard to see on a piano roll without careful inspection.