What is a reason for catalytic converters to be attached to transmission

The mounting brace Part No.: 20711-AF40A is used to attach firmly cat converters to the transmission - for that reason, a small part, which holds the bolt to attach both ends of the mounting brace to cat converters, is welded in to cat converter's body, but during the time it became corroded so heavily that is it actually does not exists anymore.
Right now, there is no physical connection between the brace and cat converters on both ends of that brace and, as a result, the brace lost its functionality and is no longer needed.
A question: what is a reason for cat converters to be attached to transmission? (ensure the exhaust pipes do not vibrate too much? What else?) Is it safe to leave it as is or weld in self-made part to both cat converters to restore connection to the transmussion for both cat converters?
Do other cars have something similar?
Does welding may cause severe problems with car's electronic and because of that it is better do not perform welding at all?
Thanks!