Having been amazed by the octagon of Ely cathedral I got round to wondering how many cathedrals had their towers collapse.
Quite a few it turns out. Winchester in 1107 - the central tower collapsed. They should never have built so close to the river - the entire cathedral needed underpinning in the 1900s.
Lincoln's tower fell in 1237. Ely's in 1322. Looking at the west tower that still survives, if Ely's central tower was taller it must have been impressive - and was definitely dicing with death, structurally speaking. Chichester lasted out the middle ages only to collapse dramatically in 1861.
Beauvais, probably the most adventurous technically of all the French cathedrals in its pursuit of sheer height, had two major upsets. First, the vaults of the choir collapsed in 1284. When it was rebuilt, the number of piers in the apse was doubled, making the whole thing look rather squashed and dark. Then the central tower fell down in 1573. The cathedral was never finished and the back of the transepts is still just shored up, over four hundred years later.
And at Norwich, though the fine Norman tower still stands, two spires were lost before the one that survives today.
It seems that medieval builders lived with the risk of catastrophic failure - and sometimes with the reality.