Is there a way not to have the Section Titles print in the email

When using the {all_fields} merge tag, no. However you can craft your own email by inserting each field individually into the email. Only the values will be included at that point.

Normally, you would do something like:

Name: {name:1}
Phone: {phone:2}
Shipping: {shipping:7}

You would add your own text label, then the merge tag for the value. If there were no value submitted for a field, the label (Name, Phone, Shipping) would still be shown, with a blank value. Is that what you mean?

If you want to include labels only when there is a value submitted, you would have to use a little customization in your theme's functions.php that says "if there is a value, then add the label and a value to the notification."

If that's what you're looking for, I will find some examples of how to do that.