Unfortunately this could not be further from the truth!
Retzuos start out at 15mm in order that if they begin to tear you will still have some time to get them replaced before they become Possul.
The preferable (Kosher Lechatchilah) width is 11mm according to the Chazon Ish and 10mm according to Rav Chaim Naeh.
The minimal (Bedieved) width for making a Brachah is 9mm. If a Retzuah started tearing at one spot making the connected Retzuah it less than the minimal width it is Possul and must be replaced. The Retzuah in this picture is at most 4mm.
Lesson: Do not tie the straps on very tight or wrap them on the box very tightly as this will lead to eventual ripping and invalidating the Tefillin straps.