Annulment is an earthly construct.
The sacraments are a divine construct. If you have not met all four criteria for a sacrament to occur than you might as well be engaging in a play. It may be moving or emotionally satisfying but nothing divine has occurred. If the first three criteria are met than it is up to the couple as afar as that goes and they know what is in their respective hearts.
So no an annulment is not an earthly construct, it is a formalization that the event did not occur as prescribed.
The sacraments are divine. The annulment, an earthly convenience. The process has a religious pretension, to make it palatable, but an earthly convenience it is.
The four criteria are supposedly affirmed during the sacrament - you can’t just rely on the “honor system”, and Catholics do not.
Regardless, sometimes people can’t live together regardless. Catholics need their way out, and they have it. I’m not arguing against it, just against the presumption that it is somehow more legit than any other garden variety divorce for “irreconcilable differences”. It’s a process Catholics have invented for themselves - which is fine.