Here's what I do:
1. Build two warriors in Capital.
2. Build Settler. Start work on second warrior.
3. Bring Settler and one warrior to city site.
4. Continue alternating between Warrior/Settler to found four cities or so. Early on (before 3000 B.C.), I don't see much need for the worker except maybe to connect cities with roads, being the cities aren't that large anyway.
5. When I build a worker, I max food production (preferrably farmed flood plains) for my Settler city (usually the Capital because of already high production).
I don't know what difficulty you play at, but give that a try at Emperor and see how long before the barbarians eat your warriors for lunch and kill your cities.
I tried your method as Greece. I built warrior-warrior-settler-warrior-settler. Each time I escorted the settler with two warriors then sent the extra one home to Athens. My settlers took over 20 turns each on Epic speed.
I didn't get my second city down until 2400 BC. My third city wouldn't have been much quicker (Athens was only size 4, still working unimproved tiles), except I didn't live long enough to find out -- my two warriors + settler were eaten by two barb archers around 1600 BC.
Your strategy is a ticket to disaster at mid- to upper levels. In 99% of my games I build a worker / workboat before a settler, and the time it takes to build them is repaid a hundredfold. Consider that a unimproved clam tile is worth 2
and 2
. Improved, it is worth 4
. In a small city, that is a giant increase. With two clams worked, you are making 4 more
total than before, which is essentially doubling your growth rate and construction rate for workers and settlers.
And don't get me started on the value of a worker who can pasture or farm tiles for +2-3 yield. That is gigantic. Simply put, I can get a second city founded faster by building workers/workboats before settlers, and have a bigger and better capital. The third and fourth cities will be settled MUCH faster from working improved tiles. Oh, and I'll have better units than warriors guarding and escorting. And we haven't even discussed chopping and slaving.
Try improving your good tiles before settling, and you'll see what I mean.