Unless they are completely conquered.Ending the war before the alliance has expired means you have broken an agreement
Is it merely a question of simplicity, or is the slider better for any additional reason(s)?
Justanick emphasized food production in his comment. I'm not sure how he did his calculations, and I'm not sure I agree with the value of food in comparison to science research via a specialist (it might actually be better than his calculations suggest). Cities without a granary can produce a settler every 30 turns, but they need at least 40 food, which makes for a rate of 4/3 food per turn. If a city doesn't produce at least two bonus food per turn, it's likely not suitable to put out settlers or workers on a consistent basis.
Also, we love the king day in some completely corrupt spots can have an effect. Looking at one of my old saves, I found a way to make an example:
Now the settler can get produced in probably 17 turns going from size 4-6.
Having a large number of settlers has it's advantages. It becomes possible to ICS corrupt regions for more unit support, an extra beaker or gold, getting closer to the domination limit (unless playing on a huge map) and also combat engineers. In other words, placing settlers near cities so that one can immediately shell out their defenders with artillery proper. ICS scientist farms with enough territory also can be very powerful for getting research speed up, but one will need a whole host of settlers for those, and in general the quicker the better with such.
Using just a single scientist at size 3 won't help progress getting a large number of settlers or workers up as much as trying to grow to size 6, because it means fewer tiles irrigated, and less unit support. The luxury slider won't do much in hugely corrupt regions, but in some regions at the edge of the core or just a bit beyond it maybe, it can help. Also, if you capture a city with a courthouse or police station, then it becomes even more clear that using the luxury slider can be more advantageous than using specialists.
Playing with the same save, I happily captured a city from Greece who are far from my core. Changing things a little bit after luckily quelling all the resistance in one turn I could make the image below. 3 science from city with just a police station of sufficient size. At a more favorable location, that might mean a shield. It also probably can produce more than 3 science, maybe even 5 science at size 6. And if a city produces at least three science plus whatever it needs to pay for building upkeep... but unit support gets offset that way also, why use the scientist capping growth at size 3 or 4 instead of growing to size 6?
I guess because using a scientist at size 3 ends up simpler and less time consuming. But generally speaking it's better to play turns more carefully and take advantage of long term potential edges. More "just one turn today" instead of "just one more turn..." Unless that leads to a serious loss of motivation, of course.