I think you are right, but the reasons were slightly different. At the time of the Napoleonic wars, the home front was not too preoccupied with war. That changed quite suddenly after the battle of Waterloo. Everyone with a spare room or space in the attic needed a model of the battle, populated with tin soldiers.
The reason is not so much the casualties or the parades, but the changed role of Britain. In the European framework, the country had always been second rank at best, neither as massive as Russia or Germany, nor as rich as Spain or France. Waterloo made it into a world class power. Russia, Germany, Austria, Spain, Portugal and the Netherlands had become allies and France was quickly forgiven and could participate in the Vienna Congress. That alliance would eventually fall apart, but Britain remained at the top of the food chain, while greatly expanding its colonial empire.
In that sense, I think the boxes were not just souvenirs, but also reminders of national pride, in a time when lands stopped being personal fiefs of a family of rulers, not necessarily connected by language, culture and history, becoming a nation-state, a political units of an "us versus them" character. I would have called it nationalist, rather than patriotic.
BTW, I now need to know about "onions teaching coins". Please enlighten me.
Peter