The metal band around the CRT is more than a means to secure the four corner mounting lugs. It is an implosion resisting band applied and tensioned by the CRT manufacturer to many hundreds of pounds of tension. It applies an inwards force especially at the four outer corners of the glass where the front plate meets with the funnel section. This force puts some weak spots in compression, an advantage since glass is stronger in compression rather than extension. It makes an implosion less likely, and in the event of one reduces the velocity of many of the fragments.
On an intact CRT with good vacuum, it would be unwise to remove it. On a broken CRT it still could be a bit hazardous to release the spring tension suddenly by cutting the band. On a larger 23 inch size CRT the recommended tension is 800 to 1500 pounds! 8-o Although there have been subsequent refinements, best I can tell the origins of the band and its technical functions are best described in US patent 3,350,154. Those with the interest and bandwidth can download it (943 KB PDF) from http://www.pat2pdf.org/