do you have stats on moving of dirt with buckets vs. moving with wheelbarrows? Or is this just an assumption you are making? I think probably an assumption because how often do people move piles of dirt without wheelbarrows nowadays so where would you actually have your data from?

In my anecdotal experience moving piles of dirt manually (for large piles of dirt) it is generally the digging up of the dirt that takes the most effort, if I had to move it with buckets or a wheelbarrow I would still expect that to be the case.

I would furthermore expect that there are some functions at work in modelling the moving of large piles of dirt using manual labor.

Your model may make sense with a small pile of dirt but I don't think you will find 1 remains and 2 go, at best 1 goes and you take a bit longer to move the pile.

Also, this is just my observations of having had large piles of dirt to move with manual labor (including wheelbarrows and several of those) As you scale up the amount of people you could drop by adding wheelbarrows goes down, because again the main problem is the digging. The wheelbarrows becomes a thing you trade off diggers on running. You will want to have more wheelbarrows that wheelbarrow users so that diggers can fill wheelbarrows while the users are running the already filled wheelbarrows to where the dirt is being dumped.

At this point then you would probably want to drop the wheelbarrow analogy and go to a backhoe and a truck, but then all of the various observations of the other flaws in the wheelbarrow argument become apparent, such as the factories to build backhoes and trucks, the training for backhoe operator etc. All leading to a relatively strong argument that existence of backhoes and trucks are a boost to the environment, potential job creator and those jobs will be more skilled jobs leading to higher wages in the economy.