I'll give it one more try, and rather then pick it apart word by word, please do try to take the point as a whole. Also, my math may be fuzzy, but that hardly matters in truth. The steps are still correct. Basically, what I'm saying, is if you choose to question my point because my math is wrong, I will tell you that I don't care.
This is as stark as I can make it.
Both Examples will assume that you have two cities, labled A and B, both with 10 tiles, that each produce 1 gold. (This is a touch unrealistic, but it is simply as an example to illustrate the point.)
Both Examples will also assume that you have a total maintenance cost of 5 gold. Given that you are only making 20 gold pieces, (2 cities at 10 gold a piece is 20 gold) then you are running at 25% maintenance costs. (5 of 20 is 25%)
Slider System
You have a maintenance cost of 25%, but the slider only allows for incriments of 10%. You must have your slider set at 30%. This will give you 14 gold pieces to do with what you will. (70% of 20 is 14) You will have 5 gold going into maintenance, and 1 gold going into your treasury as excess.
Now, if we assume that we are interested in doing nothing but science, then that means 14 gold goes to science. Assuming that 1 beaker is equal to 1 gold, that means you are recieving 14 beakers. If we assume that something costs 140 beakers to research, you will recieve it in 10 turns.
Now, Let's say we have a building that adds 100% in city A to science. So, because half of the empire's money is coming from each city equally, it is actually quite simple to calculate. 7 gold pieces are coming from city A into science. This means that city A is doubling it's number to 14, which means that the empire total is twenty one. As a note, this was a very simple calculation, but as more and more cities get added, it gets harder and harder to do, and as the percentages change from easy numbers to calculate, into numbers that produce multiple decimal points, it gets harder to do.
Now, let's say you wish to, for one reason or another, drop the gold earned in a city from 10 to 5. What effect is that going to have on overall science production? So the path that must be taken to discover what the overall effect on the empire is thus; Calculate the gold output of the individual city, then account for the percentage that the slider is at, take that number and apply any city bonuses to science through buildings, and you'll arrive at your number.
So, let's say we wish to lower city B's output to 5. That means you're maintenance remains the same, so you still need 5 gold to cover it, which is now 33.333333% of gold produced. Let's assume that maintenance is split evenly between the two cities, so you have 2.5 gold coming from City B, at zero additional bonuses, and you have 7.5 coming from city A at 100% which will equal 15, for a total of 17.5 science produced.
As you can see, this is tedious work, and gets quite overwhelming, especially as more and more cities get added on. As a reminder, this is what must be done every single time you wish to alter any kind of gold in any city, for any reason under this system.
Let's look at the other system.
No Slider System.
You recieve 10 gold in each city for 20 gold. You get 15 gold a turn because of maintenance costs of 5 gold a turn.
City A builds a building that gives 5 points of science. You now have 5 beakers a turn.
You wish to drop the gold produced in city B to 5 from 10. You now produce 10 gold a turn. You still produce 5 beakers a turn.
Which system would you say is easier?