What's true at each single point in time must also be true at all times, literally.
There are things that can be accomplished over time that can't be accomplished at a single time point. The links are essentially mathematical proofs that describe a very specific situation of "single winner" "single time-point" "instant-runoff (ranked)" style of election.
This is not our system. Our system doesn't use and doesn't require an "instant runoff" style ballot because there is no need for it to be "instant." In our system everyone can clearly see who everyone else is voting for and vote accordingly, allowing equilibria to be reached. Another way to say it is having 1000s of elections that compare preferences in various states provides more information about voter preferences than one election.
Also, neither "voting paradox" nor "Arrow's impossibility theorem" is in any way a proof that voting or elections have no utility or value. It is simply saying that in a very specific situation there are specific provable limitations that might seem unexpected to someone expecting some kind of perfect integration of voter preferences.