That one people can more easily check: they can go an the tower of Pisa (or a high building) and drop things.
The latter requires either taking the assertion that it's a sphere without question, or understanding the impact a non-spherical earth would have on things like visible orbits and so on. The math might not be novel (they already knew them since antiquity) but they're not trivial either.
And of course basic empirical checks also favor a flat Earth. Short of checking out and calculating orbits, or getting into some big mountain, the most basic observatiosn is that the ground appears flat - which is a good approximation to what is the actual case, given that limit of the curvature at such small dinstances being quite "flat".
The bleaker truth about evidence, facts and politics is that people are arguing for a preferred outcome, and will, to a greater or lesser extent, simply turn to rationalization (sometimes of a quite irrational type) if the evidence does not support their preferred outcome.
"Hard science" still has quite a lot of disagreements in it. The questions you cited had consensus forming quite a long time ago and are trivial now. That does not mean there was no period of consensus forming or that we do not need that consensus forming for actual current scientific questions.
Science is not limited to yesterdays questions.
Only a trivial one. Which is not really challenged.
Nobody really questions the value of the acceleration due to gravity down on Earth, or whether a body with mass X and another with Y will both fall at a rate R in a vacuum for example. And if they do, a simple experiment will show them otherwise.