I think people's objection is that you're wiping out the Yeerks in their natural form - i.e. any offspring would obviously be born as that animal rather than the Yeerk. Which... is basically eliminating any means for the nothlit-Yeerks to reproduce. That's not the same as killing them outright, but it's something in that direction. A way around that problem would obviously be to preserve some Yeerks and set up breeding pools somewhere, either on the Yeerks' own homeworld or some random deserted planet with no other life forms whatsoever. But that'd require portable Kandronas too. And constant guarding and such to make sure the Yeerks didn't run around infesting Gedds and start the whole war all over again.

But, yes, I love the idea of morphing sentient creatures, I think it'd be the cleanest and most humane solution of them all. It has its problems (again, as humans they're more potentially dangerous than as, say, cats), but it would definitely be a huge bonus for the Yeerks.
Someone mentioned Yeerk hosts infesting the Yeerk nothlits; again, it's not perfect, but it's a good idea.

The problem is that we don't know what happened in canon, We've no idea how much the Animorphs and the Yeerks themselves had a say in this. The bloody Andalites could've done anything just for expediency. :(