There’s no need for the puppet paired with her to be intelligible since Angelo seldom adds anything important to her recipes. If it were up to me I'd phase out Angelo and phase in the Swedish Chef.
Eh, you don't watch many cooking shows, do you? I'm serious... a good half (and I might be underestimating) have some assistant (sometimes even the host) stand there and do nothing while someone else cooks, asking only inane questions and only contributing REALLY bad and forced jokes. Though, if the character's supposed to be a parody, the satire is pretty subtle in that aspect.
HOWEVER, what they did in the last 2 episodes with the character quite improved what they had... he showed a tiny bit of contempt for other characters and their incompetence (Andy and Randy especially... but also Beau), and the fact that he himself screwed up and made a huge sandwich and spent the entire rest of the segment cowering, nervous and twitchy, even taking it personally that it was a failure really gives the character something besides the "I'm here for some reason" borderline Marty Stu-ishness.
As I said, I actually don't want to see the Swedish Chef unless he has no filter. I don't want to see some watered down role where he's basically the dummy cook, handing her the wrong ingredients and muttering mock Swedish asides. I want to see the same culinary catastrophes that made him so funny in the first place. That doesn't mean he can't fit in. I'd like to see another minute added on to the show where he takes the recipes too literally and gets clobbered by them. So, the best choice for co host would either be Kermit or any rotation of him, Gonzo, Fozzie, and (what the heck, if they can get David for a little bit) Scooter. And make Angelo the incompetent side kick or something.