Johnathan.... it is possible to get a non-clipped wave and have it be as loud as it needs to be.
Compression is just one tool to get you there BUT.... using too much compression will remove all the dynamics from the song and the listener ends up with ear fatigue from the constant continuously high levels with no relief.
It took me a while to get the formula close to right... keep dynamics and still be radio ready with the levels.
Generally, my first few drafts will look like the wave you show..... shaved tops, but in the tracking and mixing stages that is OK.... and yeah.... I have put out more than one song with shaved tops.... no shame in that.
Now that you've heard a song that has dynamic range and no clipped/shaved tops and still is loud enough to rock...... you have defined your next goal for your own music. I'll be watching and waiting.