Because the machine heads want our protection. They're fairly friendly towards us, they hate the 504s, and we're the ones keeping the 504s off their backs.
The machine heads are the smaller of two chained dogs, and we hold both of their leashes. Of course they'll want to come inside the house, eat our food and share our beds. Especially since we keep the 504s as outdoor dogs.
Simply put, you assume way too much subserviance, and way too little attachment to their homes and way of life. Do they have a guarentee of actual democracy and independence if they move...where? Shattersaw, I suppose, which has an elected president but also a leader's council that they aren't a part of. They'd be giving up a moderately strong (if hardly stable) position for a weak and uncertain one, and for our part we'd be handing the 504s a massive amount of land and resources.
If we were forced to move right now we'd leave behind all sorts of resources, technology, and the like. The Machine Heads will be no different in that sense, other than just sabotaging or destroying all of their stuff before they move, and if they don't do so, then the 504s get access to a lot of new resources that I doubt they'll share with us at all. Why would they? We know from word-of-QM that had we waited even one more turn for Confederacy, the 504s, feeling locked out of the loop, would have sided with Space Nobles rather than accept being completely subservient. So I'm not sure I trust strengthening them and weakening the Machine Heads, which is what the move would be in the short and medium term, and I'm not sure, if I was a Machine Head, whether I'd trust us THAT much.
I mean, try to look at it as a player, would *you* accept that sort of deal? I wouldn't, because it's not a sensible or sane one in that it gives you very little, lets the enemy you've been fighting walk away with everything, all for the vague promise of a new life in Shattersaw...governed by a council that includes your enemy on it.
Edit: Also, on another note, Dat Natural 1 for childbirth. God, our luck sucks sometimes.