Ah, good point! Without enough essential amino acids, you’ll have a surplus of non-essential amino acids and the liver can only store so much, so your kidneys take the hit and have to get rid of it.
Just keep in mind that incomplete proteins =/= only non-essential amino acids. Incomplete proteins also contain essential proteins, just not all 9 of them. Though, I would need to look up actual breakdowns to get a feeling for the essential / non-essential ratios.
I did look up some more information on the metabolic cost of processing proteins and it seems like there are more energy costs involved than I was taught in uni. Next to breaking down proteins into amino acids, there’s also the conversion of amino acids into other amino acids, protein synthesis, folding, transportation, posttranslational modifications and other processes.