I understand how you feel OP, i.e. that your children are being punished for something that you feel, rightly or wrongly, is your fault. None of us are perfect.
You could try sending the message you have suggested. It isn't unreasonable in itself. However, they might say that they get many such requests from parents and really cannot give in to them all. So you would then have to accept that they must do the detention.
There are two things you could have done differently here if you felt that their lateness was your own fault and wanted to mitigate it.
Firstly, you could have driven them to school and had them there on time.
Secondly, if you weren't going to drive them you could have phoned ahead to the school for them, said that they would be a few minutes late, that it was your fault entirely and it wouldn't happen again.
My DD (now in the lower sixth form) was unavoidably late yesterday because the bus arrived almost half an hour late and due to being at work neither DH nor I were able to take her. She phoned me (I couldn't work out why she didn't phone the school herself, but never mind) and I phoned the school for her. She signed in ten minutes late in the end and there was no issue.
You could have driven them. However, I don't think it should be beyond them to set alarms themselves too.