There are times when getting the first settler out ASAP is not necessarily the best.
I haven't played many games on Immortal, but I have found on that level, and to some extent on Emperor, that getting the first settler out too quickly can involve too much risk ... if you are going to go the chop route, you have to research Bronze Working. You may also need to research techs like Agriculture and Animal Husbandry, and lacking copper in the capital, hunting and archery for defense (because the barbs show up quick and in numbers). Quite a few archers may be necessary to defend both cities, causing some military upkeep plus the maintenance on the second city, slowing techrate.
Add this in, plus the necessity of either getting pottery for some cottages, or writing for libraries(expensive) and scientists (cut production), and just allowing the capital to grow to size 4 or 5 while building military and allowing the worker to improve tiles (mines, pastures, farms) rather than chop wood can give a more manageable start.
BTW, I am not suggesting you should not build a library and run some scientists ... that is a good idea just to get an early Great Scientist. Just that if you get in a position where the tech rate is slow early on a high level, you may not have the hammers to spare on a library and specialists.
I used to use the worker/chop worker/both chop settler strategy a lot. Especially on Vanilla (when chopping before math was stronger). Now, I tend to make sure I get the capital growing and its tiles developed. Getting the capital up to size 5 or 6 very quickly, working all improved tiles will allow building more workers and settlers quite quickly, and this is when I tend to start chopping settlers. This allows time to build some military and tech pottery and the wheel so that one (or both) of the first 2 cities can be working cottages just about right away to pay for more expansion, more military, and a higher tech rate.
Up to Emperor level for sure, it is not necessary to always have the 'optimum' early game strategy. But it is important to have a strong strategy and not make big mistakes that set you way back. Some examples of big mistakes:
Starting with a settler for your first build. This is a mistake because a second city won't help nearly as much as having a worker improve the capital's tiles. After the Settler, you still need to build a worker, and it will be a long time before your capital (or your second city) produces much at all.
Growing to size 3 or 4 before building a worker (excepting the case of having fishing and a couple seafood tiles where it is ok, even ideal). With no seafood tiles, building warriors and scouts (have even seen people start with barracks as first build) until your city grows bigger than size 2 is again a very big mistake because extra unimproved tiles aren't worth much. It is occassionally a good idea to grow to size 2 before starting on a worker, but don't delay it any further.
Even when using the worker/chop worker/ both chop settler strategy (which is still good in the right cases), it is usually better for the initial worker to improve a strong resource tile (if you have the tech) before starting to chop. Any tile that provides 5 or 6 Food + Hammers improved should be improved before chopping. If you have 2 such tiles, and are going to build worker 2nd, you only have to improve 1 because you can't work both at size 1. Tiles that should be improved ASAP are copper, pigs, sheep, cows, corn, wheat, and rice if it is on a fresh water tile. If you have 2 such tiles, and the tech to improve them, I would suggest improving both and growing to size 2 before chopping the second worker. Example: you start with Agriculture and have a riverside corn tile, then with BW, copper shows up in capital. Improve both and start on a warrior while you grow to size 2.
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