If you search through the forums long enough you'll find reports of fires every year. Lemme see if I happen to have any bookmarked... well that didn't take long:
https://www.backyardchickens.com/threads/coop-fire-advice-needed.1555495/ Granted this isn't in a brooder but the point remains that they can cause fires or in this case, a lot of smoke.
Just to clarify I use a heating pad, not a plate, and yes I still have a heat lamp in the garage as a backup (which I had to use once because I got chicks a day earlier than expected and needed to keep them warm while I got the heating pad set up!)