#1 is correct, but #2 is wrong.
During war, gold is useful in Civ as it can instantly create units. But science is better in the long run (a heavy science build can get ironclad battleships by 0AD in game time)
The FreeCiv governor is a solver where you input your goals (maximize science vs maximize gold) and then the solver solves the optimal placement.
But it only works if the human gives it the right goals.
Even with a science focused build, a city in rapture will generate more science. But do you solve for rapture conditions? Or do you solve for science optimization?
Is there a key science that will increase happiness (temples, banks, colosseums?). Is so, maybe having a short term science focus for some +happiness is going to be overall faster.
What if one city has more gold buildings? Should this city use the same solver as the rest of your cities? Or do you want this one city to focus on gold and let the rest of your cities handle science?
If the solver fails to solve for your conditions (ex: no starvation is a common solve condition. But maybe my enemies are pillaging my farms and starvation is always going to happen now...) How does the solver react? Should it reduce starvation as much as possible? Or should it stop and point out the problem to me?
Maybe I can't rely on food supplies in that city and need to build caravans to import food from a nearby city. The governor doesn't have control of units, only of the city. Maybe I need gold in my other cities to buy caravans to send food to the starving city, while far away cities continue to focus on science.
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EDIT: It should be noted that the Governor can sometimes be unhelpful. For example, if you have two cities within a rare "whale" tile (whales are one of the best tiles in the game), only one of those cities can benefit.
The governor of the two cities will fight for the whale, meaning one city will randomly not get the whale.
In such "fighting" situations, you disable the governor, then manually choose which city gets to work on the whale-tile, and then turn the governor back on. The governor is only "locally optimal". It still requires the player to make globally optimal decisions (ie: a bad choice for city B means city A benefits more, and maybe you have multiplicative bonuses in city A (due to trade routes, buildings, specialists etc. etc.) who can benefit from the whale more than B ever could).
Choosing to make "city B" play suboptimally is a strategy, to make your overall civilization more powerful. The governor doesn't have such insight, and must be disabled entirely in these situations.
That's what makes "using" the governor so hard. Its "just" a locally-optimal solver.