I have a similar thought too - whether some cells that express the spike proteins would get destroyed by the immune system. I asked this question in an email to Dr. Pascolo, and I discussed his answer in this article too.
Based on animal studies mentioned in this article, the vaccine-induced expression of spike proteins only lasts for a few days. So, I think that the spikes do degrade quickly in the body. Notably, one study (link below) did show that the spike protein alone (not vaccine-derived ones) degrade very quickly in the body. Assuming the immune system attacks the cells that express the spike proteins, I believe this would also last for a few days only, and the damage done won't be extensive.
But please note that these are based on reasonings only. I think when it comes to science, it's rare to say anything conclusively and we rely on theories most of the time.