My understanding is that the most productive biomass crops in temperate latitudes are grasses not trees. So I don't think your argument about the sun collecting efficiency of a taller crop stacks up. It can't collect more sunlight than there is, and a low-growing crop can do that just as well.

We do have tree "grain" crops. They are usually called nuts in English, though this is not a valid taxonomic description and many languages do not have this word. Examples include pine-"nuts", chest-"nuts", wal-"nuts", almonds. Ground almonds are key part of mediterranean pastry cooking, often replacing much or all of the flour. In Corsica, or at least in the NE part of it, chestnut flour was the staple cooking flour at one time. In southern Chile, a sub-tribe of the Mapuche people called Pehuenche (ie, people of the pehuen - observe that "che", same as in che Guevara) used the "nuts" of the monkey-puzzle tree (pehuen in Mapudungun language) as their staple, huge nuts they are too. Acorn flour and beechmast has been eaten at times, too. Coffee, cocoa and carob are all "tree grains" too.

I suspect that yields of tree "grains" cannot compete with grass "grains" in terms of yield per area, nor for convenience of harvesting. Pinenuts, chestnuts, almonds, cocoa, coffee, etc, are extremely expensive in comparison to cereals. But possibly as a side-product of the wood, they might just be worth collecting.