Sorry vs Thank You

The other day I was driving to meet some-one, I was late, and I noticed the yada yada voice in my head saying "I'm sooo sorry I'm late, I got a call, and then I couldn't find my glasses..." and I realised that I was rehearsing my excuse / explanation for being late, and I began to wonder how useful the whole groveling apology thing is.
And then I realised - an apology looks like it consists of concern for the other, but actually (as a friend used to say) -
"I see your lips moving, and all I hear is me me me me me."
So when I arrived, I said: "thank you so much for your patience". He really didn't care about my rush and fluster, he was far more interested in getting on with the task at hand.
And why do I share this? Because our brains tumble endlessly over the me me me, and then we assume that others care.
For instance, how do we expect clients to engage with websites that say:
... with over 50 years of experience ...
... one of South Africa's leading ...
... we are committed to Africa ...
... me me me me me me me me ...
We hope folk will give us money - just for being fabulous?