The impracticality of totally eliminating alcohol consumption
Alcohol occurs naturally in the food we eat and the drinks we drink:
Ethanol production has also been observed under natural conditions in such tissues as germinating seeds, fruits, and root tips. -- Cossins and Beevers, Ethanol Metabolism in Plant Tissues, Plant Physiol. 1963 (link)
...ethyl alcohol contents of different kinds of beverages, vinegars, vegetables and fruits collected from Turkish markets were investigated ... the ethanol contents of fruits, vinegars and beverages were found to vary between 0.32x10-4-0.35% (w/w), apple vinegar and concentrated orange syrup were determined to contain as high as 0.44 and 0.68 % (w/w) ethanol, respectively. -- Gunduz, Yilmaz and Goren, Halal Food and Metrology: Ethyl Alcohol Contents of Beverages, J. Chem. Metrol, 2013 (pdf)
Consequently, this discussion is not limited to Coke, etc., but foods and beverages as a whole. We are forced to accept some level of alcohol consumption (barring some ultra-restrictive diet). Thus, we are forced to either accept (a) some level of permissibility of alcohol consumption, or (b) sinning in the form of alcohol consumption being unavoidable.
Moreover, even if we were to somehow avoid consuming alcohol, our bodies ferment it regardless.
The human body constantly produces small amounts of alcohol itself. Normal levels of 0.01 to 0.03 mg of alcohol/100 ml are contained in the blood. -- Alcohol allergy, Australasian Society of Clinical Immunology and Allergy (ASCIA)
Small but definitely measurable quantities of alcohol are normally present in many parts of the human body: in the liver, brain and blood; from bacteria in the large intestine; and in the muscles. -- Ibrahim B. Syed, Alcohol and Islam
Surveying the online fatawa, revealed the following overall theme:
- If a substance is incapable of intoxicating even in large quantities, then it is not haram (insofar as to being an intoxicant). Some add the caveat that the alcohol in drinks should also not be derived from dates and grapes.
And I think it's safe to say that Coke, etc., is not intoxicating even in large quantities, at least, as far as alcohol is concerned [the sugar, caffeine, and artificial ingredients in it may be another story]. And, as far as I'm aware, is not derived from dates and grapes.
What follows are some pertinent fatawa (there are many others online, so my search was not exhaustive).
These specifically address soft drinks:
The contents and procedure of making the Bundaberg brewed drink as explained by yourself is the same as other soft drinks. The alcohol amount is minute and is from sugar cane and not from grapes or dates. Such soft drinks are permissible -- AskImam.org about Bundaberg ginger beer
...since the alcohol in coke is from ethanol which is fermented from sugar cane mollasses and does not intoxicate, it is permissible. -- AskImam.org
Generally speaking the alcohol which is found in soft drinks is chemically made and not extracted from grapes or dates, thus it will be permissible to consume the soft drink. (Ahsanul Fatawa p.488 v.8) -- DarulIftaBirmingham sourced from IslamQA.org
...if the alcohol in the soft drink is made from anything other than grapes and dates, it will be permissible to consume the soft drink. -- Mufti-Online.net
The above fatwa quotes Muhammad saying "Alcohol itself
is prohibited and intoxication in every other beverage." (which I cannot confirm as authentic; so I asked here).
Related fatwa in various other contexts:
"Whatever intoxicates in large quantities, a little of it is haraam" means that if a lot of something will cause intoxication, and a little of it will not cause intoxication, then a lot or a little are both haraam, because you may drink a little that does not cause intoxication, then you may be tempted to drink more and become intoxicated. But if something is mixed with alcohol but the alcohol is a small amount and does not have any effect, then it is halaal and does not come under the ruling of this hadeeth. -- Islam Q&A, 33763, in the context of beer
...non-alcoholic beer... though there is a trace amount of alcohol in certain brands... this minute amount does not in any way warrant classifying the drink as an intoxicating beverage. It would be extremely difficult for a person to drink enough of the beer for the alcohol within it to have any affect. -- IslamToday.net
The incidental presence of alcohol (from non-wine sources) does not make an item haram, as long as it is:  Not being used to intoxicate;  Not being used in an amount that intoxicates;  Not being used as intoxicants are used;  Not being used for vain (i.e. useless) purposes. -- Qibla.com, sourced from IslamQA.org, in the context of naturally occurring alcohol in fruit
Ice creams generally contain such a small percentage of alcohol that could not intoxicate, thus if the alcohol is from corn and is in a minute quantity, then it would be permissible. -- AskImam.org about ice cream
However, the above opinion was not unanimous, but far more common. I encountered a single fatwa taking a contrary stance, which specifically addresses soft drinks:
All beverages that contain ethanol based alcohols are unlawful to consume. If a particular soda contains alcohol, then it would be unlawful to consume no matter what the amount. -- Islam.ru
(NB. I did encounter contrary stances to non-alcoholic beers and vinegar made from wine, which weren't relevant to the Coke discussion.)
The IslamToday.net fatwa, in the context of non-alcoholic beers, gives this way of understanding its ruling:
Sheikh Salman al-Oadah astutely observed: "The percentage of alcohol mentioned has no effect on the ruling. The ruling applies to the drink itself taken as a whole and not to its composition."
While even a drop of alcohol may be forbidden, and while Coke, etc., may contain a drop of alcohol, we don't separate the alcohol out and drink it---we drink Coke as a whole.