I know where you're coming from, but I'm not sure I agree.
Traditional medieval cathedrals were built right on the limits of the materials, skills and labour available and still took generations and sometimes still collapsed due to overambition: especially lantern crossings, which are heavy and only supported in the corners.
Builders of cathedrals used the cutting edge tools and techniques of their days. If they'd declared, say, vaulted ceilings "cheating", they wouldn't have done what we see today.
I don't see a tension here: to them, perhaps, the monks are using skill, tools and material God made available to them to do the best they can (also considering the labour force God has not given them). Rejecting God's offer of tools that can make a better cathedral would be like a medieval architect swearing off a horse-powered crane to get a heavy keystone in place.
And for that matter, Gaudi's Sagrada Familia is only as complete as it is due to CNC stone cutting and other modern machinery.
I just wish, considering these kinds machines exist, that we could have them used to make beautiful building again in general, rather than always plumping for a variation on a glass-and-steel box (perhaps it's simply about the cost, but I do wonder if it's also about what's even possible to draw in AutoCAD for a normal architect!).