Here's some discussion of the topic. Including a respected instrument maker who would deliver a ringing bell or a dead one to the customer's preference, without comment.
Bell ringing - does yours?
I also recall a report in Scientific American where bells made from various materials were compared. A stainless steel one proved unrewarding to play, one made from lead gave a bright sound (but obviously had practical disadvantages!)
There are basics of instrument construction - the physical dimensions and arrangement of the tubing, the flare of the bell - which I think can be agreed to be predominant factors in the instrument's quality. Then there are details which can border on being fads - heavy clamps to 'couple' the mouthpiece and mouth pipe, bell sections stripped of lacquer... I tend to put ringing/non-ringing bells in this category. Pay your money, make your choice.