Exogenous topical steroids are mainly used for maintenance. They are very effective for long term use and does not have significant systemic side effect. Meanwhile oral steroids were used to treat severe acute flares with the risk of its side effects.
Stress has several pathways to trigger eczema/dermatitis and not only cortisol (endogenous steroid, stress hormone).
upregulation of neuropeptide mediators in the brain, endocrine organs, and peripheral nervous system directly affect immune and resident cells in the skin
Increased mast cells and mast cell-nerve fiber contacts
sensory nerves release neuromediators that regulate inflammatory and immune responses, as well as barrier function.
In summary, several underlying mechanisms results to the effects of stress towards eczema and cortisol is released by the body to help and combat some of eczema's inflammatory response. We treat eczema with steroids to help our endogenous steroid reduce inflammation.
Source:
Psychoneuroimmunology of Psychological Stress and Atopic Dermatitis: Pathophysiologic and Therapeutic Updates
Andrea L. SUÁREZ, Jamison D. FERAMISCO, [...], and Martin STEINHOFF
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3704139/
P.s. Eczema is a poorly understood disease with no definite treatment, all we have for now is symptomatic relief