Sorry if this is old news, but I just found it today
Go to m.google.com/sync on your iPhone or iPad.
Select which device you want to change the settings for.
On the next page put a tick against Enable "Delete Email as Trash" for this device and save the settings.
Now when you delete an email it is moved to your bin/trash instead of staying archived in All Mail.
Again apologies if this is old news, but I though I would share it.
Hopefully someone might find this useful
Go to m.google.com/sync on your iPhone or iPad.
Select which device you want to change the settings for.
On the next page put a tick against Enable "Delete Email as Trash" for this device and save the settings.
Now when you delete an email it is moved to your bin/trash instead of staying archived in All Mail.
Again apologies if this is old news, but I though I would share it.
Hopefully someone might find this useful