Why isn't the insertion of a single nucleotide destructive for DNA?
A single substitution can often be silent, or at least not impact the structure and function of the resulting protein in a significant way. But what you describe is a frameshift, and that is one of the most destructive mutations. It will completely change the sequence of the protein after this mutation and disrupt the function of those parts of the protein.

Insertions or deletions that result in a frameshift are absolutely destructive mutations.