You didn't understand correctly. "Rationalist", in the OP, is a historical label which can retrospectively be applied to a specific set of thinkers, who defended specific beliefs, from the 16th to the 18th centuries.
None of them were claiming they were the only people who thought "rationally"; rather, they were mostly claiming that only rational thought could reach truth, and empirical evidence need not factor into it.
In modern parlance, the Rationalists believed that all knowledge would end up being deductive, like math.
> Gödels theorems are hardly ever relevant to most of mathematics and not in the least to computers (which are finite).
https://en.m.wikipedia.org/wiki/Halting_problem
> I also doubt that industrialism has anything to do with Leibnitz or Hume. That part of history is most likely fuelled by greed for money, not for philosophical thought.
In this time period, the intellectual circles that Leibniz and Hume frequented are exactly the circles that gave rise to modern economics, the ability to measure longitude at sea, the ability to calculate rates of change over time, using steam to power machines, etc. In other words, we're literally talking about all of the intellectual developments that directly led to the industrial revolution.