A well applied lime wash is something more people should be aware of in the modern world. If you live in an old stone building it is what you should be using for exterior stonework and not modern paints!
It is not the problem with lime vs another white paint outside of the buildings. Modern paints based often containing TiO2 are more durable.
But I am with you that using lime especially on roofs/sun exposed walls (assuming lime does not eat up some materials) before summer is sensible if done correctly. Otherwise we will have a spike in hospital admissions of ppl splashing lime over themselves.