There's many things to consider in terms of trees and their role in a bushfire. There's many pros and cons.

There's nothing good about bark mulch near your house. It's just as bad on the ground as it is on the trees and will produce extensive and prolific ember load to the structures.

If the bark mulch is actually adjacent to the structure itself it can also provide so much heat that it can crack windows and ignite decks and facades and building elements, just simply at that adjacent proximity.

Smooth-bark, very clean-bark Eucalypts that are virtually shiny finish, have little to no bark hazard at all. Whereas other types of Eucalypts thick fibrous bark can present a very high acute bark load, which is a main source of embers.

If you manage the fine-fuels, and especially the fine-fuels that form structures that connect the ground to more elevated fuels, you actually take out the seat or base of any fire. Certainly, the canopies of tall trees can't get involved in a fire and can’t really contribute if there's nothing underneath to support the flames base. I good rule of thumb is clearing surface and near surface fine fuel so you can freely walk around under the trees.