-concidering it is in the middle of a city there are basialy no wild animals
-this isnt more dangerous to the remaining few than any 4 lane Road
-there are city maintenance workers who take care of the trees
-during realy bad storms there are also branches on the streets
vs
1 billion different advantages
The actuall biggest problem would be leaves on the rails in autumn.
A small brush system ahead of the actual wheels could take care of some of the tree debris. Even a small to medium sized branch would probably have no effect, the tram is heavy enough to just cleave branches apart. The negative of that is the maintenance teams probably have to clear out stuff that gets stuck under the trams.
There are plenty wild animals in large cities. Foxes, rabits, racoons ... Berlin famously has a large boar population. Having a more human friendly city with green tram lines and less car traffic will surely increase animal populations.
However I doubt it would be a problem that isn't easily solvable or is still preferable to the current situation.