Ah, yes, you've found the root of the matter! Einkorn wheat is diploid, unlike most (or all) of the other cultivated Triticum species. I'm planning to attempt a cross between Agropyron cristatum and Einkorn, to hopefully get a grain very much like Einkorn, but perennial.
There are a couple reasons for this:
1. Einkorn has a better nutritional profile than other wheats, and its gluten is much healthier for humans to eat.
2. It is generally a more resilient crop to grow in terms of handling
pests and drought. And its tightly hulled grains may help keep fungal diseases out of the grains.
2. Einkorn is the most primitive of the cultivated wheats, so I'm hoping it is easier to perennialize.