I’m guessing you could give the available_sections a value that is an array like this:

'value' => array('Default 1', 'Default 2', 'Default 3')

This code produces the attached screenshot for me (Piklist 0.9.9.9, WP 4.6):

piklist('field', array(
  'type' => 'group'
  ,'field' => 'classes'
  ,'label' => 'Classes'
  ,'add_more' => true
  ,'fields' => array(
    array(
      'type' => 'text'
      ,'field' => 'class'
      ,'label' => 'Class Name'
      ,'columns' => 12
    )
    ,array(
      'type' => 'text'
      ,'field' => 'members'
      ,'label' => 'Members'
      ,'columns' => 6
    )
    ,array(
      'type' => 'text'
      ,'field' => 'non_members'
      ,'label' => 'Non-Members'
      ,'columns' => 6
    )
    ,array(
      'type' => 'text'
      ,'field' => 'section'
      // ,'label' => 'Section'
      ,'add_more' => true
      ,'columns' => 12
      ,'attributes' => array('placeholder' => 'Section Name')
      ,'value' => array('Section 1', 'Section 2', 'Section 3')
    )
  )
));

But when you say it “doesn’t seem to work as a child add more,” perhaps you are referring to this limitation:

Currently, default values for our Add-Mores only work on the initial field. We have it on our list to make it work on every add_more.

This means that if you add an additional class, it won’t display the three default sections. Only the initial class will show defaults.

@Dan I owe you an apology because I posted all that forgetting that I had applied this patch, So I wasn’t working with a clean copy of Piklist. When I revert that patch, I see the exact same problem you described.

I guess it’s up to you whether to modify the Piklist core files with that patch. Again, my apologies.