Ignoring the question of whether the government should actually be involved in this, I don't really see why this specific aspect of society should be opt-in. Basically all things provided by the government are used at different rates (or not at all) by different citizens so I don't see why that reasoning wouldn't lead us to making all things in society be opt-in. Some actually believe that sort of idea makes sense, but I certainly do not.
In any case, the government could surely just regulate private nursing homes much more strictly making many of these parasitical companies' business models untenable.
In reality, people don’t really care much about very elderly people. Not even their own families most of the time.