Tripods used to come in very convenient collapsible sling bags. They weren't padded, but they allowed one to sling the tripod over your shoulder. If you needed to use the tripod, the tripod bag would come off, and in it went into your back pocket, no worries.
Nowadays, all the tripod bags are all ridiculously overpadded. I think the manufacturers are simply bending to the demand of the tofu consumer who can't take the touch of metal on their skin. If you take the tripod out of the bag you will have no real way to stow the tripod bag properly unless you have a car. Some people will throw it to one side first, but that's not so convenient if you are shooting right by the sea/beach.
So I carry all my tripods by hand. I'm thinking of getting Think Tank UD series with the tripod attachment straps so that I have an option of strapping the tripod onto the bag temporarily when I need both hands, e.g. when scaling the steep slope of a mountain to get a view during travels.
The super padded sirui tripod bag is heavy, so usually, I will tie the tripod with the padded sling. 1 end goes to the "neck" of the tripod, the center column below the ball head and the other end goes to the legs.
As for carrying it, just sling it, but when my shoulder is tired, just hold it with my hand instead.
i carry it this way too...but i don't have the luxury of paying someone to slave like that for me... nor do i want to do it that way.. God gave me two hands, and two feet.. and a strong back along with everything else to carry my tripod and other gears.