On a full flight there's really no need to check at all. If too many people board you'll catch it when the spurious passenger tries to take a paid passenger's seat. And if identity actually mattered (hint: it doesn't), well it's already been "screened" via the purchase and TSA checkpoint tests. Planes flew for decades without any matching of passengers to tickets, and tickets were frequently resold (especially unused…
Planes also flew for decades without locks on the cockpit doors, but that doesn’t make it a good idea in the modern world.
But I haven't seen any actual justification that the no-fly list is actually useful, and worryingly the regulations around it are classified.