Yes, fair point, the "ent" is literally something like "de-," so you are "de-blaming" yourself or "freeing <subject> from blame."
But in common parlance, I think the phrase "Ich entschuldige mich" is really meant more to say "I apologize" than anything else. I guess this could be a place where descriptivists and prescriptivists differ in their interpretations (and I lean a bit more towards being a descriptivist).
I haven't studied German society closely enough to know what people really mean with this phrase, but this is how I've always interpreted and used it, and other people seem to use it in this manner as well.
Instead, you're supposed to say 'Ich bitte um Entschuldigung' (I beg your forgiveness) - thus you're asking the person who was wronged for forgiveness. It should not be the choice of the wrongdoer to decide whether to be forgiven or not. Though to be fair, commonly it's used just as you described.
If I remember correctly, Kraus has at least once written about this specific phrase.