Odum's system has numerous problems.
One is that the "transformity" (ratio of emergy to energy) is path dependent. One ear of corn might have been produced with more or less water or fertilizer, both of which contain more emergy than the sunlight that falls on it.
Another is that you can't trace all energy to "the" sun or at least not our sun. The energy of Thorium and Uranium in the Earth's crust probably came from two other stars that became neutron stars and crashed into each other.
Emergy accounting does a good job of accounting for externalities of consumption (e.g. trace back water use in Central Valley agriculture to Shasta Lake) but doesn't do a good job of accounting for the production of noxious influences.
The latter may be intractable, may really be the death of environmental accounting, because instead of producing one number for a product you produce numerous numbers. How can you compare 1 g of tetraethyl lead in the air to 1 ton of CO2? A megacurie of Krypton 85 to a kilogram of PFAS?
There is a field of "multiobjective optimization" that considers these problems but leaves as many questions as answers in that different people are going to see the trade-offs differently.
(It reminds me of the doomed project where I was working with some people to create an "NQ" score for the nutritional value of food and we couldn't get consensus on how to combine factors. For instance it is good to eat riboflavin but you can't give nutritional yeast, which colors your urine bright yellow with riboflavin, a score proportional to how much riboflavin it has. It wasn't clear to us if it really made sense to evaluate individual foods... You really need to eat protein/Vitamin C/Zinc if you haven't had any today, you don't need to if you have. We weren't even sure you could assign it to foods w/o reference to portion size... One scoop of ice cream is not so bad but the whole box is something different.)