Time to train a model matters for applications where you want to have end users training models on their own computers without spending so much CPU/GPU time that they have to plan their day around it.

Consider for instance an RSS reader that classifies articles to determine whether or not to interrupt the user with a notification. This should be fast to train and update the model on the fly every time the user enters a correction (e.g. 'this article actually isn't interesting', or 'interrupt me with articles like this in the future'.)