can always throw down 2-3 mines and easily get that 20

/turn
No. That is the point that I feared (rightly) was a bit unclear in my post. When I'm talking about 600 "extra" beakers (or 20 "extra" bpt), I mean 20 more than you would generate without alpha. If you start working a river-PH-mine you will be making 5.25

(with lib), but it's only 1.5

more than a scientist that would yield 3,75

. So 20 extra bpt is actually quite a lot, so there's many cases where Alpha isn't worth it, especially if you go for Monarchy first.
Better than cottaging non-river grassland?
Depends.. If happiness is very limited (no HR), then mines are definitely better than non-river cottages (didn't build a single capital cottage in the Sally game). With HR I like to grow to either
- Health cap or a bit above if there's a lot of food. Better to run scientists when food surplus reaches below 4

- Work only the riverside (if the rest is coast or plains / hills). Absorb the food surplus with scientists/mines
Also, when you have Alpha, riverside mines become very strong tiles. River-mines are then always superior to non-river cottages. However I still like grass cottages to grow to health cap. Kinda depends on the situation..
Regarding barbs... do you have a clear target like "control island by ~T60"? Some specific questions...
Not really. I usually kinda wing this, but the main thing is I look at the really screwy places where a barb Archer could spawn and I fogbust them. Then I mostly make sure my second city is safe, which often turns into placing one defender inside the city and waiting for barbs to attack. Don't forget that warriors get +25% city defense and an extra +25% "city barbarian defense", which gives them winning odds against Archers with just 5% fortify bonus.
Maybe this could help you (made this a while ago when trying to figure how to deal with early barb Archers) -
1) Let's say there is an area and you "know" there is a barb archer there... What do you do? Especially in tundra/ice with no good positions... if I just wait "at home", I will kill him, then just a new one spawns. So how to solve this? Rush him?
There usually is a forest hill somewhere, even if it's a bit further away it's not a problem. A barb Archer's vision range is a 9*9 square around it, which is how they find your city so quickly when they start rushing. So he'll see your warrior even if it's quite far away and will often follow it. However this does not always work. The sure thing is that the Archer will head towards your city at some point, the best is if you can find a forested hill in its way, or have a hilled city (ideally in a spot where the Archer wouldn't smash too much improved stuff).
So this kinds boils down to 2 steps:
- Have a warrior play chicken with the Archer until you hopefully reach a forested hill and kill him
- Have another warrior waiting for him in your city in case it doesn't work or if you get killed. It's good to have another warrior replacing the one you lost and ideally killing the wounded Archer.
But then again, it depends...
2) In early game... when moving your first warriors, some leaps of faith are needed, no? For example entering flatland to reach next forest. Do you take this risk for potentially much better position?
Yes, you have to move out in the open at some point. But the thing is that you are taking a
small risk for a
big gain. I'm not sure what the probability is of encountering a barb Archer on T10 when moving your warrior on flatland, but it's pretty low. And even if it happens and he kills your warrior, it will still fogbust the area until you send another guy to kill him -- barb Archers don't attack cities extremely early.
Not sure if you know that, but barbs won't enter your borders as long as the number of (non-barb) cities in the world is below or equal to 3 times the number of players. This means
barbs won't enter your borders until every AI has 3 cities and 2 of them have their 4th city settled.
The main exception to this is that a barb will always enter your borders if he can attack one of your units on the same turn.
even on that big Toku map (where you got late Optics), you managed with warriors. So it should be possible quite often..
That was an exception, actually. I was playing an AGG leader, had a lot of excess hammers and built Barracks+Cover-promoted Warriors. This allowed me to take out quite a lot of Archers in the forest and on forest hills. With a "normal" setup, an island like this requires Archery
Btw I looked at the Izzy game. I think that using the marble would be optimal, especially with such a high commerce start. Will try it out. However I don't understand your capital's position. Did your warrior not reveal the rice on T0? If it did, then there was every reason to settle 1S2E. If it didn't, then I don't understand your logic behind moving the initial unit.