I agree with these steps as presented with the exception of number 2. There are many instances when offering an explanation is nothing more than patronizing commentary....and that makes the situation worse.
So, I would add that an explanation can be given if there is a known circumstance that allows for an explanation, otherwise, just say that there is no excuse or explanation for the issue...we blew it....and go on to number 3 and how it will be corrected.
Word processors have made it easy to insert scripted paragraphs into replies, for sure It is a fact of life, and will be so for a long time. When was the last time any of us got a hand written note of apology from a hotel after a bad incident? Maybe never?
Apologies are nice, sincere apologies are better. Good comment TEF