All have a part to play
Rather it must be seen as something much more important. There should be involvement in the affective domain as well as the cognitive domain. There must be the developing of values and the preparation for and actual involvement in community at local, national and global levels.
In addition to modern studies there is a vital part to be played by geography (I teah this as well), by history (I have taught this), by social education (and this!), by modern languages, by maths et al.
The reality is that teachers teach children and as part of this all teachers help prepare pupils for citizenship - nursery, primary, secondary, tertiary.
If education for citizenship is to be a priority (I think it always has been just not the "flavour of the month", as it is now with politicians) then it is exactly that we must strive for, argue for, campaign for.
It must not be seen as an argument for individual subjects. This surely shows a narrowness of vision which education for citizenship stands against.