Self driving vehicles too slow?

Have any of you had to drive faster than the speed limit to get a passenger to their destinations quicker? I've had a few times where people asked me to drive them quicker to get to their destinations because they were late for work, getting to the airport, going to a meeting and one time to the ER. I drive early mornings where's there's very little traffic and ended up driving 5-10 mph past the speed limit to get to their destinations. They all ended up tipping well after. I only do this if they specifically request. I realized self driving vehicles aren't going to drive past the speed limit if it's "breaking the law". The take off seems pretty slow compared to human drivers too. As soon as the passenger gets in and shuts my door I'm already going. When these self driving cars roll out everywhere, do you think people will get fed up with how slow it'll take to pick them up and drop them off?