Interestingly one of my pet peeves about the grocery store is that I must ask to get help putting groceries into my car and then they sometimes look at me like I have two heads for asking. I sure don't enjoy not being able to do such things for myself but sometimes I have to. Fortunately I only have need to shop once a month.
I guess this one differs between people. I would get quite angry if someone tried to put my items into bags or if someone tried to help with taking my full shopping bag to the car. I don't want someone who I can't be sure will order my items properly to do my ordering for me and I don't want someone who might not treat my products properly handling them any long distances. I sometimes even wince at cashiers who might scan a tray of eggs and then just push them harshly away to make room for other items. And I am saying all of this as someone who works as a cashier himself. I myself take great care of how I handle peoples groceries and I take extra care if they have products like eggs, cold soda, flowers, clothes, celebration cards and other such products they may not want to get dirty, shaken or mistreated in any way. And I never put into bags unless I am asked to do so as I would expect other cashiers to do for me. A local store once hired people (mostly teens) who had the sole job of putting groceries into bags for customers but it only lasted a week or two before they were removed because of bad receptions. I myself went there once before I knew they had hired people to do that and I didn't notice until my grocery bag had almost been filled and the person filling it was doing it all wrong so I had to spend time picking the items back out of the bag and re-arranging them again while checking each item for damages.
As for helping to take groceries from the register to someones car where I work at least there just wouldn't be time in the day for that. The moment I'm done with one customer another is there to replace her or him, and so it can go on for the entire day. It would slow down the traffic out of the store massively and would create a problem with queues. But if it was a slower place I work at where there would be time for that I'd still wait to get asked as I myself would not want someone to handle my bags, I guess they could ask but generally people wouldn't want the help so it would be less of a bother if the few that did would ask rather than if the people working there asked every single customer just to get barraged with "no" with just a few cases of "yes" here and there.