The level of credulity displayed here is pretty amusing.
but just to back that up:
https://en.wikipedia.org/wiki/Skellig_Michael#History
Not a cathedral, No mention of an appearance of St Michael, and the monastery predates the dedication to him (it?) by several centuries.
https://en.wikipedia.org/wiki/St_Michael%27s_Mount
Not a cathedral, site predates dedication to michael. No mention of an appearance of michael.
https://en.wikipedia.org/wiki/Mont-Saint-Michel
This one has a story of an appearance, still not a cathedral
https://en.wikipedia.org/wiki/Sacra_di_San_Michele
Not a cathedral, does have a story about an appearance, but that site significantly predates that appearance.
https://en.wikipedia.org/wiki/San_Michele_Arcangelo,_Perugia
Pre christian temple that was converted, not a cathedral
Taxiarchi Michail
Monastary, not a cathedral
https://en.wikipedia.org/wiki/Stella_Maris_Monastery
Not even dedicated to michael.