Yes, it is exactly a thing a computer virus that is designed to be completely destructive might do.
Interestingly, a biological virus can also write to DNA, but they have ADDITIONAL machinery that makes that happen; machinery that is not in the vaccines. Even in those cases it is very rare, but it can happen.
If it wasn't rare, even when it is set up to do it, the virus wouldn't have time to replicate, and on the broader scale no life could exist. Life, especially multicellular life, only works if its DNA is very rarely altered in any meaningful way.
Yes, it is exactly a thing a computer virus that is designed to be completely destructive might do.
Interestingly, a biological virus can also write to DNA, but they have ADDITIONAL machinery that makes that happen; machinery that is not in the vaccines. Even in those cases it is very rare, but it can happen.
If it wasn't rare, even when it is set up to do it, the virus wouldn't have time to replicate, and on the broader scale no life could exist. Life, especially multicellular life, only works if its DNA is very rarely altered in any meaningful way.