As Bezza mentions the corny isn't really to carbonate it, but simply to hold the beer in although you can carbonate in it.
An ale is actually carbonated unless you are drinking flat beer. If you are using pressure barrel at moment I am guessing you put your brew in and add some priming sugar. The yeast converts this to a bit more alcohol and CO2. Because the pressure barrel is sealed, the CO2 gets absorbed by your ale and becomes a bit fizzy. How fizzy is measured in volumes of CO2. Although that works fine there are some downsides - you have to get the sugar amount right, too much and your ale will be too fizzy and froth like mad when you pour it, too little and it will be flat. Also, you have yeast still in it so you have sediment and can have issues with cloudiness if it doesn't settle well.
Using a corny keg you can still carbonate using priming sugar like in a pressure barrel. However, you can also force carbonate it - basically if you connect CO2 to the keg and set the pressure, the beer will gradually absorb the CO2 until it reaches equilibrium. There is a handy chart here that shows what pressure you need for what temperature and carbonation level. carbonation chart
This has the advantage that you can put your beer into the keg already cleared and as there will be no secondary fermentation it will stay clear and you have precise control over how fizzy it gets. You can then also transport the keg without worryign about stirring up sediment. I guess you could also force carbonate a pressure barrel if you connect CO2 to it, but the keg approach I think is more convenient. They are also opaque so light does get to the beer to deteriorate it.
Given I already had the CO2 and bar font setup for commercial keg dispensing it made sense to me to go the corny route to be able to pour it out from my home bar setup.
I agree with everything you say apart from the first sentence - when homebrewing, I would say that the vast majority of people will use the corny for the purposes of force carbonation. There are some people who will still use priming sugar in a corny, but equally there are people in this world who like country music - we can't say they're wrong but best to just smile politely and let them get on with it.
Other than your case of buying commercial beers in a keg and transferring, and the growing numbers who ferment under pressure, I can't think that there's any other situation in which you would carbonate outside of the corny.