Actually, you already can do that without the touchbar :
With the regular Delete key can be done by holding down the Function, or fn key while pressing it.
By pressing Control + D.
You can delete the entire word behind the cursor by pressing Control + Delete or Option + Delete.
You can delete the entire line of text or paragraph behind the cursor by pressing Command + Delete.
But if you really want a one-press-button solution, you could use BetterTouchTool (and for $5, is almost a free option...) that allow you to make personalize shortcut ; or simply do an automator workflow to do a delete action (every workflow you make will appear on a section in the touchbar, more info here).