I think it is part of the point for a cathedral to take several generations. If you can point to a building and say "that took 5 years to build and I was there for all of it!", then that's great, but the building is in some way "smaller" than you. If you can point to a partially constructed building and say "my grandfather worked on it, my father worked on it, I'm working on it and my children will work on it too", that's a building that is "larger" than any one person.
Taking a century or more to construct anything makes that thing larger than life. There's a certain sublime quality in such efforts, whether they're explicitly dedicated to a god/pantheon but also if they are "just" earthly like the White House (technically took 178 years to construct from start to finish).
There's certainly something interesting about taking multiple generations, but it also feels kinda wrong to attribute greater meaning to something because you dragged it out or intentionally scoped the project too big.
Maybe if the project served a greater purpose and couldn't possibly be built in a shorter time, then it would mean more. But a cathedral? What's wrong with a modest church or two?
Sure, the same amount of stone could be used to construct several smaller churches. The US congress could also just rent a conference room at a nearby hotel if they chose. The Eiffel tower could supply iron for several kilometres of rail track, or maybe a small boat.
But building something extravagantly big has a signaling value all of its own: "see the glory of <whatever it is we constructed this for> and how much resources they command". You don't build a cathedral because it's more practical than a normal church for holding services and stuff, you build a cathedral to express the power of your religion and impress it on others.