As mentioned, there are toxic woods and those that simply aren't hard/dense enough to withstand the heat/flame. Obviously, briar is the predominant choice. I have a couple of Morta pipes that look nice and smoke good. I've been told to steer away from Olive wood because it can get pretty hot. I do like how some of the Olive wood pipes look, pretty wood. I believe strawberry is another wood used. I have one pipe made of Osage Orange, made by Skip Elliot, that is very pretty but gets hot rather easily.
Interesting that you talked about alternative woods used to make pipes. Strawberry wood is actually a type of briar and it's become a really popular one due to its porosity. I was talking to Jeff Gracik just a few days ago on a Zoom meeting thing and he showed us a photo of a pipe he is making of Boxwood, which he says is really hard and porous and believes it will be a good one.
Spanu is now making pipes out of Lemon Wood and while I've never tried one, they look pretty cool.