My take on it is that I don't think evolution itself will allow extinction of life. Organisms evolve to be fit for survival and so the part of where organisms cannot consume others would eventually lead to extinction does not really make sense to me when I see it from an evolutionary point of view, as said organisms eventually will evolve to have the ability to consume other organisms. Bear in mind I am not an expert in this matter and it is just my point of view which could very well be wrong.
I remember watching a documentary about an experiment that has been going on for like 3 decades that studies evolution on populations of E.coli If I am not mistaken. They used to give these bacteria multiples sources of food (glucose, organic matter etc.) and watch them reproduce. In this study, they observed at one point that the bacteria started to consume citrate (I think it was citrate but this was a while back so I don't remember the specific details) but what is interesting is that the bacteria couldn't do that before.