According to my understanding any non-chorded instrument, like a string instrument or horn, can use a just intonation, so the problem only arises with chorded instruments like pianos. So, for example, in a symphony that does not have a piano I suppose using just intonation is possible.
On the other hand, let's imagine a piano concerto. As long as the concerto is in a single key, then is it possible to use a just intonation tuning, or will there still be problems?