There was a recent project where the highway department cut down a lot of trees along the highway. I could see workers shredding/chipping the wood and just leaving the shavings on the ground. Why don’t they sell the wood to a timber company? It seems like they lost out on a lot of potential money.
WAG1 - The wood chips serve as mulch and may help reduce weed growth.
WAG2 - The chipped wood may not really have value (not the right tree species).
WAG3 - The chipped wood may have higher concentrations of toxic chemicals due to their growing proximity to the road.
WAG4 - Attempting to sell the chips is not worth the effort.
Well, they could sell the wood-cutting rights to a private company rather than selling the chips.
However I think that in some places local governments are forbidden to make money through enterprise, lest it compete with Private Enterprise to the detriment of the latter. Just as many Republicans are stopping local civic broadband in order to preserve choice.
Private Enterprise is a delicate flower.
…your OP is missing two important numbers: how much it would cost to collect, distribute and sell the wood chips, and secondly how much revenue would be generated by selling the wood chips.
Until you bring us those numbers, there really isn’t a lot to discuss.
What happened to The Most Holy Free Market? 
Does the wood necessarily even have to be chipped? If they are cutting down trees, they could sell them as lumber.
Maybe local companies don’t want that kind of wood.
Seriously, how the hell are we supposed to know what the deal is about some wood near some road in some county in some state?
Typically they are crap trees with little value. We just had some big trees taken down. We discussed disposition. We didn’t want/need any wood. The cheapest bid was for six trees chipped and removed, one tree they took the wood (and charged less for it), and one tree was left laying for a neighbor who heats with wood and wanted that tree. He then cut up and hauled the wood out.
Chipping wood or chipping brush and or overhanging limbs ?
Where i live most of the highways have a well defined boundary that is mowed every summer so there are really no trees growing there. What i see now and again is the DOT to go by and trim the overhang and such and that is chipped.
Trees are not created equal. Lumber is generally created from just a few species, a few additional are harvested for special purposes. This is a highly efficient industry with benefits of scale producing material of predictable quality. Hundreds of other species exist. Making lumber out of them would be a venture with higher cost, unpredictable results and unpredictable sale value.
The same applies, albeit, I’m guessing, with slightly less risk, for firewood.
ETA: And that’s even without examining the question of how not all trees of the same species are created equal. As several people have already mentioned, the trees could be a commonly harvested species, but of crap quality.
And even if maybe some of those trees could have had value as lumber or firewood, it’d cost money to find out.
Trees from the sides of roads (and people’s yards) are somewhat undesirable from the standpoint of timber companies because they are much more likely to have metal in them – possibly from old signs, barbed wire fences, or even bullets. If an old bolt or nail gets through the metal detectors and hits an expensive saw blade, well, there go the day’s profits.
I’ve done it and had it left as mulch, but all of Duckster’s options are on the table for this work.
Do you have an example where this is actually the case anywhere in the U.S.?
In terms of state & local government accounting, there are GASB standards on the accounting treatment. They’re even called “Enterprise funds”, where a governmental entity provides goods or services on a fee basis.
Common examples include municipal parking garages, community swimming pools, water utilities, and airports.