Think of anatomy as a tool you use in your drawing process. Focus on composition, gesture and values, then bring structure and anatomy in later to 'tidy' things up.
The main way anatomy has helped me is to understand what those lumps, bumps and shadows actually are. This can help if I want to change something slightly than what I see, but still keep it believable.
When it comes to cartoonish styles, the main benefit is the understanding of overlap. Eg, I know that the pectoral muscle goes over the top of the biceps, but inserts under the shoulder muscles. Now, this can be simplified with a slight line at the armpit to show this, but it can be kept small if the person isn't muscular. It can also greatly help if there is foreshortening. Knowing what muscles will show in front of the other, will help when you have that hand reaching out to the picture plane, or that leg as the person runs into the distance.
It can also help when using perspective. I know that from looking from below and upwards, the chest comes out a certain degree and will overlap the neck (maybe even hide it altogether) and you will only see certain features of the face.
So keep it loose, but when you aren't sure how something would look, refer back to your knowledge, and use it to make those slight adjustments.
Hope that helps.