I have a "particular" set of requirements since I do all my stuff in an urban setting, alone. I will post the "routine" in case someone has a better way.
The chain is pretty destructive on everything it is dragged over, including the bed and the ramp. Going across concrete or hot top with 400-600 pounds of log and 3/8 chain makes a mess.
Going up the ramp or through the mud (because of the high angle) it does not want to stay on the bottom. Especially the larger pieces. Then the log either flips or goes sideways. I have used the 3/8 chain for moving very big (31 inch dia.) pieces into my truck, but, the chain is awkward and destructive compared with using lags.
Most of the time, to lift or roll a log to fit a chain around it, especially in slippery GA mud, is not worth it. Especially if I am working on an incline. Though I have been thinking about the cant hook/timberjack things since my breaker bar does not hack it moving logs.
The other thing is cost and weight. If I kept enough chain for each log (6-8 feet), I would end up with another 50 feet of chain. It takes me 45 minutes to load my truck in the morning with my tools. Lugging some more chain out, besides what I already have, is something to avoid since those 5 gallon buckets get heavy

A lot of the time I line up all the wood I am taking at the end of the day and then shuttle back and forth getting it with all my tools put away. I would feel uneasy leaving $200+ worth of chain laying around near a sidewalk where anyone could get it. If the tree is on the street, I usually cut my logs large so noone can load it onto their truck/car without extra mechanical or human help.
Losing a few logs and lags will not hurt as bad as losing my chains to anyone that can roll a log. If you know what I mean.