Because his proclamations turn out to be right time after time after time. As for past proclamations being overturned by future prophets, is it your assumption that the world is static? No institution can survive if it is unwilling to change in a dynamic environment.
That seems an oddly pragmatic view of religion. The
Shakers, for example, who flourished about the same time as the LDS church, have all but died out, because they chose not to give in to the pressure of the world.
They took the opposite tack, requiring celibacy for all members rather than encouraging reproduction, and when religious groups could no longer legally adopt children, their main source of new recruits dried up. There were
three members left, as of a couple years ago.
But still, they didn't compromise. As one of the current members said in the interview linked above: "So we are celibate because Christ was celibate. We live in community because Christ and his disciples lived in community. We’re pacifists because Christ was a pacifist."
The Shakers have chosen to let their religion die out, if that's its fate, rather than to change it to fit the world.
I don't see why that's any less a sign that they're the one true religion than the LDS church, which
has adapted itself to be popular. I don't think either is actually getting instructions from God, of course, but I don't see that being adaptable is necessarily a sign of a good religion, or even required of a religion.