You can request, but you will be denied unless it's a safety issue. For example, there is a sewer drain that backs up with ice every winter and the carrier's vehicle often gets stuck. The carrier would request that the rack of boxes be moved, and USPS would come out, look at the situation, and agree that it be moved.
In your case, the reason for the request is for personal convenience. That request will be denied. It is less efficient to deliver to five separate boxes than to service five boxes in one spot, and if that was allowed, you would still be parking in front of your own box and not getting your own mail. Moving the rack in front of someone else's house only transfers your problem to that person. Is that really how you want to live, dumping your troubles on someone else?
Now, if there is an area on the cul-de-sac that is not in front of anybody's house, is located in a safe location for the carrier, and does not change the existing sequence of delivery, USPS would probably agree to that request. It would mean everyone would have to walk to that spot instead of to the front of your house. Talk to your neighbors and see what they think.
Anytime a box is obstructed so that the carrier cannot drive up to it and drive away without having to back up, the carrier is specifically instructed to NOT dismount to deliver the mail.
The first concern is safety - it is less safe to stand in the street and deliver mail than to do it in the protection offered by the vehicle. Last week in our area, a garbage truck backed into a woman taking mail from her curbside box and killed her. If someone hits you while you are in your mail truck, and it has happened to me three times in my career, you are a lot safer.
The other reason is that curbside delivery routes are very different than walking routes. On a walking route, the carrier has time to have all mail for an address to be 'box ready', and a foot carrier must only carry three bundles of mail, flats on the arm, letters in the hand, and a third door-to-door mailing in the satchel. The motorized carrier can have five or six bundles. The carrier must get that mail for each box from those five or six different mail trays and have it all together in one handful to place in the box. There is no way to safely or efficiently do that while standing in front of boxes.