Ich möchte einen Kaffee trinken.
Sie will in die Stadt fahren.
My textbook says that when the context is clear, it is possible to omit the infinitive. Thus, above sentences may become
Ich möchte einen Kaffee.
Sie will in die Stadt.
Can we so omit the infinitive in both formal and informal situations?
Yes, it's possible to omit the action from a modal expression if context makes it clear what is meant. It's also perfectly fine to do so.
In fact, it often sounds much more natural to leave out the action. German native speakers do it all the time. The only place you shouldn't skip it is most kinds of narrative, because it sounds like a fake reportage style then. Too natural.
