Here and there I read that the Free Church tradition including Baptist congregationalism contributed to the development of constitutional democracy at least in the USA.
Of course Baptits would argue rightly that they do not practice a democracy but congregational discernment of the mind of Christ - a theocracy - yes - but discerned and interpreted by the congregation. This said the above point of the thick practices of the Church having a thin application in the State perhaps stands.
Of course 'democracy' is not a uniform thing and comes in many shapes and sizes. Not all democracies equally allow people to be represented. Projecting from the Baptist thing - of course the issue is not about representation but about participation and responsibility. To be sure many Baptist 'meetings' and 'practices' do not necessarily encourage such. Be this as it may this is surely the goal.
In turn while democracy is better than no democracy - the Baptist projection of the thick practice of congregational discernment into the thin practices of the State should favour those approaches which enable the greates participation and responsibility of its citizens.
The above said we probabaly have to admit that we have a bit to go in Baptist Church life to develop the thick practice of the kind of congregational discernment and decision making processes that can bear effective witness to the State as a sign of the Kingdom come.