I did misunderstand the type of city you had in mind. What you describe is certainly a commerce city. However, with only 1 seafood in the BFC the lighthouse only really gives +1 food, since I'll not want to work a coastal tile while there is a cottage to grow (even though it might take 10 turns to give 2 commerce). Is 60 hammers for a lighthouse worth more than an earlier library or courthouse? it's not an obvious choice and depends on the stage of the game and what is needed from this city. That +1 food will take a long time to pay back the lighthouse investment. If it was 2 seafood then I'd go for the lighthouse first and +2 useful food to fuel whipping and growth, that would be a good city.
In the short run the CH can win; but in the short run cash can beat the CH so I find that long term I want the +1 food for getting to (more)towns faster. This is more about working more tiles and growing cottages faster; for one seafood we can debate specific instances; for two the lighthouse is normally superior to the CH.
Obviously depends on how many cottages they can have. You must play different maps from me.
Most islands seem to only have 4 grasslands and 3 desert, a seafood and then coastal tiles. A weak commerce city that I only build up if I'm desperate for income. After Chemistry I often build workshops on them and turn them into whip / draft cities.
I play a lot of fractal and shuffles with the odd tectonics/ice age thrown in. I get games where I think I have a large landmass if it fits 3 cities and I've had pangeas where I literally couldn't REX to the coast. Most of the time I cottage if I know I'm going to be going for a rushbuy economy or if I get to the island really early - I can either whip, use it as a lousy GP farm, or cottage it.
Again it depends on the number of seafood. With 1 seafood you only gain 1 food until you have to work the coastal tiles. A granary first and then either a courthouse or lighthouse. It's not clear to me that the lighthouse is better than a courthouse - that obviously depends on how much the courthouse saves; which is maintenance and inflation dependent. In some of these low food situations a lighthouse would have to be whipped before the courthouse since only coastal tiles are food neutral and getting to size 6 for a 3 pop whip of the courthouse would not be possible otherwise.
I build the LH for one of two reasons - I have a lot of cottages to work soon and the 
let's me grow much faster or I want to whip expensive things (like CHs) and the LH makes that more efficient
I usually lightbulb part or all of Education so I'm well into Liberalism before I can build UoS even with stone and a good production city. That means any boosts from monasteries or temples of the state religion have a small impact on the outcome. I like monasteries in my commerce cities, the +10% for only 60 hammers is good value especially in deficit research. Having a few (obsolete) monasteries is useful in the late game when using spies and running Nationhood and Theocracy (EPs and drafting powergame) as having my state religion in his city can give big discounts on espionage missions (even more with the shrine). Manipulating religions with espionage is powerful in the lategame.
In recent games I seldom get all three of the AP/UoS/SM until after Sci Method has made monasteries obsolete. I frequently build UoS, seldom build AP, although I do get it spread to me, 1 game in 3 maybe, and SM is always a prime target for an invasion with cannons plus whatever I can scrape together. That usually means I end up with temples being the only widespread building getting all three bonusses and it's well into the end game, useful but not gamebreaking.
I'm not sure what the "obvious reason" is
perhaps you'll explain. I have studied the effects of trade based games extensively and have written a lot about the GLH. For me leveraging the GLH depends a lot on how you manage the domestic trade routes rather than the foreign ones. For instance if you only have 15 cities and they each have 4 trade routes you need 60 foriegn cities if they are all to be lucrative. Typically taking account of war, diplomatic problems and Mercantilism I'm lucky to get 20 foriegn routes (and I'd have all of them with or without the GLH). The GLH effectively adds 30 domestic trade routes to the economy and shifts a few foriegn routes (sometimes to better cities).
When you want to bulb astro you need to gimmick with the techs open; for instance philo gets bulbed before astro. Avoiding CoL can make it far easier to push out the bottom path, quickly, and get the bulb to Astro. Virtually all of the time this is before banking; if you can get to econ or better communism (which comes quick and easy off a swap to the lib path) before the AIs get heavy into rep, then a lot of AIs will stay out of merc.
Wars, well those are just opportunity cost questions until the AIs get Astro.
The harbour can add +1 commerce to some foriegn trade routes but not others.
The usual trade factors affecting the value of trade routes are:
+25% connection to capital
+100% overseas
+150% foriegn trade (actually grows 3% / turn after a war)
+50% harbour
For a basic foriegn city of size 10 (or less) it would give 3 commerce without a harbour and 4 commerce with it. A harbour helps here
But if the foriegn city was size 11 (so trade route base value is 1.1) then it would give 4 commerce without the harbour and a harbour would not add enough to take it to the next level. (so your recollection is not good
)
Is the actual value truncated or does it just display the truncation? My point more is I've never finished building a harbor and watched my net output drop.
The size of own city also adds +5% for each pop over 10. So if our city is size 15 city it gets +25% that combines with the connection to capital bonus and a size 10 foriegn city gives 4 commerce (so again a harbour is not useful for this trade route)
Trade routes are a complicated subject and thinking that a harbour always helps is not true
. In fact it can hurt large inland cities with good economic modifiers. A weak coastal city can have better trade modifiers due to a harbour and hence get better trade routes than an inland capital with Oxford and an academy. This is not desireable.
I have never witnessed this. Whenever I've built a harbor my reported net output has increased or stayed stagnate; an actual overall fall is something I have never seen (note with heavy CE play this may just be the cottage growth disguising such); I'm not saying that a harbor is necessarily better, just that it ranks up there. Getting one 
per trade route + health can be better than the savings off a CH' the cheaper cost and easier whip is also a factor.
Sure, I hope our discussing these ideas helps other people.
. In that circumstance a courthouse wins over a library and it continues to give its benefits regardless of the slider setting. The benefit is overtaken by a library later in the game when the cottages mature but as the city grows and the empire increases the number of cities the benefit from the courthouse also increases.
makes CHs better investments, . However given that libs come earlier than CHs, early GSc are cheap and extremely useful, and that early 
Obviously there is a period of the game when a library is available before a courthouse and I certainly build them then, but that is outside the scope of the OP's question 
) that libraries boost overall research by 25% when this is diluted by other cities with no library where commerce has a zero multiplier.
tile that can "borrowed" from an overlapping 
modifiers in other cities).
; you get out of strike sooner; you upgrade all your CRIII trebs to cannons. All of these make the long run return higher for a "short term" investment.
