So you dont build Granary or Any hammer boosting buildings in your

city?
Why would the city need

if it doesn't need to make anything the rest of the game?
And, I said Granary is probably the most advantageous. If only because it lets the city grow in size slightly faster (and thus work more tiles faster). But, if happiness goes up 1 at a time and the city can keep pace, even a Granary isn't necessary.
So when you fight a war and slider goes to 0, this city will contribute nothing??
If fighting a war requires slamming the

slider to 0, doesn't that indicate a lack of preparedness on the part of the player?
Or, that the player doesn't have enough

specialized cities (which itself indicates a lack of preparedness).
(In any event, a
cottage 
specialized city will always contribute base

, so it will
never be literally "nothing". And, a
specialist 
specialized city will always contribute the same base

, regardless of the

slider.)
Hammers are extremely important to EVERY city, you build the hammer buildings early, so that when better city improvements (university,observatory, lab) become available, you can get them build faster.
What's wrong with chopping, whipping, or cash production? There's nothing faster than any of those. In fact, they're quite a bit faster than working mines, so your implication is exactly wrong.
And during war, your

cities can at least build spies and contribute to your empire.
Why in the world build units in a city with no

? We can crank them out in a

specialized city with no problem at all.
The only time I can think this would be useful is, again, if the player was unprepared and needed the production queue capacity.
Production queue capacity is the ONE big disadvantage of city specializations. We don't want to churn out units in

cities... we want to make them in

cities, and especially in cities with Heroic Epic etc.
But that's inherent in the strategy. If you don't like that limitation, then play with the non-specialized strategy, or play with a hybrid (with Forges and mines in

specialized cities).
When the games are tight, there is nothing wrong with having lib/uni/obs And mkt/groc/bank in you top commerce city because they significantly boost both the

and

output of that city when slider is in the middle.
You're assuming the empire is a CE. When, in fact, it's much easier to do city specialization with a SE for the precise reason you mention.
City specialization can be done with a CE, but what ends up happening in my experience is that any

specialized cities tend to the GP farm or secondary farms. i.e., the empire tends to be a a bunch of

cities, a bunch of

cities, and one

city (the GP farm).
And when you only have the luxury to build 6 cities, you need hammers in every city so you can unlock those powerful national wonders.
You're probably talking about just Wall Street and Oxford. We can chop/whip/cash buy those.
Forests are the best option... after all, what
else is needed to be chopped there? The City only needs 3-4 buildings if it can skip a Forge, AP buildings, and the rest of the non-essential stuff.
Specialize but be flexible, build things that you NEED. there is nothing wrong to build Markets/Grocery in your large production cities to raise happy/health cap so they can become even more powerful. After all, they can get those things build quickly anyway.
I don't have a problem with that. After all, the opportunity cost to crank out a market in a

city is extremely low. See above where I mentioned a cost:benefit decision before making a building.
But regardless there's also nothing wrong with using the culture slider to solve all happy problems, or simply conquering more resources.