I'm currently in the US and haven't tipped anyone yet.
It is possible to avoid it without offending anyone.
As uncomfortable as it is for us to tip, it is a way of life for many of the underpaid workers in the US.
I have an American friend who works in the tourism and hospitality sector. She said that most of the house maids, waiters etc, are paid the minimum wage of $2 per hour. They rely on tips.
We did a 3 week tour from NYC to New Orleans. Our coach driver, is paid $15 an hour. He will only be paid a maximum of 11 hours per day, regardless of the time he is on duty.. Often we would see him packing the suitcases at 6.30am in the morning and many a night he would be picking the group up from some venue at 10.30pm. He kept an esky underneath the coach always stocked with bottled water and ice. He would clean the coach out at the end of the day. Often we would see him washing the coach down and blackening the tyres, he kept it pristine.
He was an excellent driver, always friendly and courteous. The tour was 21 days long and he only got one day off in the middle of the tour. $165 maximum per day is not a big wage, but never once did he mention tips or gratuities.
Yellow taxi drivers in NYC have to rent the taxi for $120 per shift and pay for their own petrol use. Whilst in Charlotte we had a bite to eat in in a pizza place. We got talking to our server/waiter who was a young African American young man who had been on a football scholarship but due to an injury his football career was over. He was waiting on tables for free to get some experience to put on his resume to gain work, so he was only working for tips. (He did not tell us this, a policeman eating at the pizza place told us).
So yes you may feel that you are not offending anyone, but you may be affecting them.