If I remember rightly the intent is that the embryo actually changes the host DNA so the host's body doesn't fight it off.
Absolutely vice versa! How small cell is able to change the whole body? It's too expensive, much easier is to change itself (one cell). If no, then there's no meaning in drone variations such as Runnners, Predaliens etc. That is why embryo borrows host DNA - only to hide. Other abilities like extrastrong or extrafast are consequense of that borrow.
Life example: When you run away from killers, you will hide in garbage can and dig into it, but never change the whole street. Maybe you're able, but they are running after you and you have no time.
So is here. Embryo is growing too fast to change whole environment, much easier is to hide behind host's security systems.