It is established policy that we should not fertilize an unhealthy tree. That statement appears a couple of times a day. I wonder why.

Potassium helps fight off disease, and weak trees need help fighting disease, so why not?

Phosphorus helps build roots. If repotting damaged roots, the tree might benefit. Similarly with trees with roots killed from heat.

Trees that gave dropped leaves might benefit from nitrogen to stimulate gr.

Is there any experimental data showing damage from fertilizer? Or benefits?

If the tree is not growing healthy it is not absorbing much nutrients. Fertilize then risk a buildup to levels not healthy for the tree.