I’m sure I’m not the first person to consider this method of simplifying travel with a baby.
It would be well worth the checked bag fee, though it would need to include a warning: Caution — Live cargo; beware of teeth!
Checked bag
Whole Health Dietitian — Tastefully Fueling Active Transportation
Her Green Life 
That is classic. Wouldn’t it wonderful if it was THAT easy?!? (Not that I EVER would!) Mine would happily travel in a laundry basket or a cardboard box. š
Ha, I wish! Our first of four flights total (2 out, 2 back) was actually pretty smooth. The remaining three were interesting, especially the final one where it was like sharing a seat with a wild animal climbing all over me.