Catalytic converter

In order to reason objectively, the detected error code is necessary.

A constantly lit check engine light is dangerous because you get used to it and can miss a serious problem.

 

You can't damage the valves, if the car is running rich. You can fry the CAT if it's running rich or you have excessive oil burn. We can't see, smell, or hear the car over the internet, that's why we're asking for error codes.

There's a communications issue here. Either you misunderstood what the mechanic told you or the mechanic is full of CRAP. As I explained above. There's several ways to kill a new CAT or that CAT was defective. That's why we ask for the error codes. A good, professional repair shop would've checked for those other issues, before installing a new CAT; because they need to warranty their work. If a customer drags in their own part and tells them to just replace this. That's all they're going to do. The only warranty your going to get is that it won't fall out of the car.

@MAX2 stated; if another fatal issue crops up; you won't know, until the car just stops running - since your CEL is already lit.