I see couple issues off top of my head:
1) Street tires will still be street tires; low grip and screech around everywhere.
2) Bald tires = low heat sink capacity; they will overheat very quickly, and will have past the prime of their lives. It'll be tough to keep them in their optimal temperatures for a predictable handling.
3) More susceptible to damages from longer period of wear and tear that they've gone through.
4) If it rains, pretty screwed. And if you can afford a second set for wet, then why not just use those for dry also since most UHP or EP tires that are great on wet are also great on dry.
5) I don't think you'll pass tech inspection, since this is re: safety.
If you're talking about moderately bald, like 3/32 or something, you can prob churn out another day or two. But if completely bald, prob not the best idea.