However is much more efficient to purchase that settler and / or workers if you need them. So you are actually saving gold, not production.
500

is a lot to throw at a Settler. It's a more attractive play than it was, given the rebalance in early building

costs, the new

->

conversion factors on early buildings and the weakness of city-states early on.
I've been known to buy a Worker in a city where I need to hook up luxuries and can't reasonably walk a Worker over or steal, but I try to exhaust all other options (and plan ahead on my steal) before resorting to purchasing the Worker.
That isn't really fair as you are saying that monarchy isn't as good as 2 separate policies from liberty. If it is true (and I agree that it is) that monarchy provides as much happy as meritocracy, then is handily beats meritocracy.
Yes, but the problem is that Republic beats the pants off of the

from Monarchy (it isn't even remotely close once you expand), and the Tradition branch has dead policies. Monarchy alone is better than either, but the combination of Republic + Meritocracy is far superior to say, Oligarchy + Monarchy or Landed Elite + Monarchy.
A tradition build, on the other hand, can grab monarchy to easily mitigate a lack on unique luxuries and keep going. Republic may grant 3 or 4 extra

but a tradition captial can easily produce a way more than that because it's simply much bigger.
It's a question of what you can build. CiV still has the same basic problem that it always has: you want the first tier buildings and Universities everywhere because they're

efficient and cheap to maintain. Everything else is situational. Further, you get far more

per unit of population in many small cities than in a few large ones due to the way the

mechanics work. The only exception is if you managed to build the Hanging Gardens amongst a bunch of Hills. The result is that in almost every case the small cities are much more efficient producers. You have fewer citizens but they work better, more efficient tiles, and the

they make gets sunk into more efficient buildings.
Why would they get more raw science or culture? On the science front its intuitive. A tradition player will have a larger captial, and therefore get more out of a captial library and the NC, which BTW they save turns on thanks to aristocracy.
The

math has always favored spamming cities and Scientists on several levels. First of all, a Scientist under Secularism is nearly
eight times as efficient at producing

than a citizen assigned to a tile. Second, adding more cities running Scientists yields up more Great Scientists. Each additional city past the first is marginally less productive, but it's still sensible to slap down another city as long as that city will end up yielding a Great Scientist that you otherwise wouldn't get before the end of the game.
Liberty's +1

/city is okay but that doesn't really mean they have more culture. Liberty players have to build monuments and temples the same as everybody else. Oh except that tradition can get 4 of those buildings for free.
Right, but since you want four Opera Houses in a Culture game, you can't go very far in Tradition due to tech limitations. In any other game, Temples are pretty hard to justify due to the

maintenance unless you have a Temple-replacement UB or get something more expensive like a Wat from Legalism.
But again tech limitations are a problem there, which forces you to run the Tradition/Liberty split in order to get the UBs.
If you're not getting a powerful UB from Legalism, a GE is a lot to give up in order to get a couple of lousy Temples from Legalism and pick up Monarchy. I can see how you might want to just take the four top-quality Liberty policies and go elsewhere, but there isn't any combination of policies in Tradition that's going to compete with what that GE can do.
Games exist where taking Tradition itself for the border pops is sensible, and it's best to recognize that your map is going to compel this early. Taking Tradition to accelerate early policies is a horrible long-run play that incurs substantial late-game costs, but sometimes you don't have much of a choice. That's one of the stronger arguments for aggressive scouting; if it's going to be one of those games, you want to know soon enough to take Tradition with the first policy.