Done and Archive are incompatible. Delete.. Delete..

If you ever want to delete a G-email from its notification itself in your Android phone (may be in iPhone, too), set 'Delete' as a default action instead of 'Archive' in Gmail app and 'Bin', instead of 'Done' in Inbox app.

Gmail notification

Email deleted

Inbox notification

At present, no undo for Inbox app

Steps!!?

Find it yourself. It's there in settings.

Well, if you are a dummy...

In Gmail app:

1. Open settings from left navigation drawer
2. General settings
3. Change 'Gmail default action' to 'Delete'

In Inbox app:

1. Open settings from left navigation drawer
2. Your email id
3. Under 'General'
4. Change 'When removing messages, I prefer to...' to 'Move to bin'

This will also change the action when you slide a single email in inbox from left to right in Inbox app and both sides in Gmail app. It will show delete/bin button in Android Wear notifications, too.

[Cyberman image source]