financial cottage economy is very situational compared to a specialist economy.
how often do you find yourself without food resources? you normally get corn, fish, wheat, cow, clam. they are very abundant everywhere on any sort of map.
of course. if you are playing financial and regenerate to find a map with a lot of rivers, riverside grassland and floodplains, then you are set. but very often, your start will be on a lot of plains and hills, and the rivers are far away from your capital. (i do think regeneration is cheating)
you can pretty much play on any map with a specialist economy, even if you are river deprived. i think financial is horrible if your initial cottage can't immediately become 3

. So i think financial only shines when you are on rivers, and when you have rocky city sites, financial isn't much of an advantage.
of course, a specialist economy will allow you to create a great prophet faster for your shrine, if you ever own a holy city.
SE = always awesome. =when you have food.
and CE = situational. =only when you have CE-friendly tiles (riverside grassland, floodplains)
Floodplains is awesome for SE too.
so SE is more adaptive.
according to the Darwinian laws of natural selection, CE can be weeded out.
Then let them weed it out for Civ V. For now, Civ IV would have to die before any sort of natural selection would take place... As it stands, CE's are effective on a tremendous majority of starts in Civ IV, so they are far from dead.
I run a primarily cottage economy effectively on Emperor/Immortal play in at least 80% of my games. You suggested that CE's are only effective when you regenerate the map until you get a good start for it... The truth is, a vast majority of starts are CE viable, so little to no regeneration is required. Grasslands are ridiculously common. You insinuated that plains are no good for a CE, which is a mistake, as they make good hybrid squares - you just need food to support them. As you pointed out though, food is not hard to come by. Flood plains, of course, are great, and hills are necessary for production, so they don't detract from a cottage economy, they add to it. Unless they compose 90% of your squares, of course - and even then, one straight commerce city + one straight production city is almost as good as two mixed cities in a CE, so the odd city that is almost all hills works quite well in a CE. The simple fact is, you can run an effective cottage economy with pretty dry, crusty land, much like an SE - you just need food, which as you pointed out, is all over the place. Thus, financial is very powerful on a majority of CE viable starts - which is a vast majority of starts, period.
Oddly enough, the only real place where CE's don't work are on water heavy maps (not plains heavy, like you suggested) which don't allow you to build many cottages... And financial shines on these maps. Non-specialist economies are very viable on these types of maps too, but since you aren't actually relying on cottages to do the heavy lifting in such cases, calling it a CE is a bit of a misnomer, even though it may not be a specialist economies... I find hybrid economies are my flavour of choice on water maps anyways.
Two of your biggest misconceptions are these... One, that rivers are necessary for a CE. They aren't - far from it! They're a perk, and that's it. Secondly, you say that "think financial is horrible if your initial cottage can't immediately become 3"... The period in which a village has yet to grow one size is a tiny, tiny, tiny portion of the entire game, meaning that the Financial benefit will be in effect for a *tremendous* majority of an entire game. This makes the financial benefit very substantial without a river in your civ if you're running a dedicated CE.
So yeah, Financial is "horrible" for the maps which won't allow you to run a cottage economy effectively... Which for me, on Big and Small Snakey continents islands mixed in random climate type, is *maybe* 1/10 times I play - and I'd guess it's notably less than that. Usually a start that I can't run a CE in is some tundra craphole which would hardly provide enough food to run a half decent SE either.
Anyways, good for you - you enjoy playing a specialist economy. I'm sorry to say that, your statement that financial is a horrible trait is utter and complete hogwash in anything but very rare circumstances. Unless of course you prefer playing SE's, which is the case for you. CE is not "very situational" compared to a SE, as you stated - it's very slightly situational. In 9/10 games that a SE will work, a CE will work just fine. That other 1/10, I'll go SE. Don't go telling new players that the most popular trait in the game is "horrible" because of what "experts" think - many very experienced players disagree with you. Also, do you think maybe you haven't given CE's enough of a try? It sounds like you consider certain strats throw aways, for CE's, which could be kept and cottaged up quite effectively.