Does pasta dough really need to rest?
You didn't knead it enough in the first place. 2 minutes is too short even with the pasta machine afterwards. 

Pasta, especially the classic semolina pasta (which is mae with durum semolina), is a high-gluten product. To make it correctly, you need to develop that gluten. I don't make semolina-water pasta, but knead my flour-egg pasta for around 8 minutes. It makes a great dough, and you can feel the change in texture while kneading. Of course, dough with that much Glenn is way too tight to work it. Very hard to roll, resists cutting. That's what you need resting for: to relax the gluten. Else, shaping becomes a heavy chore. 

There is no food police which will come to arrest you if you make noodles with underdeveloped gluten, but most people prefer the slightly resilient texture of developed-gluten noodles. You describe yours as "having a great bite", and apparently they didn't fall apart in the boiling water. So you could make both side-by-side and decide which is more to your taste. I you stay with the ess kneading, you will need less to no rest.