It seems to me that most of the complaints about register windows is related to the need of managing them via software, in case of overflow or task switch. What

It seems to me that most of the complaints about register windows is related to the need of managing them via software, in case of overflow or task switch. What if there were an streaming hardware unit, with it's own caches, that managed that, similar to the spiller on the Mill? Wouldn't register windows then reduce the load/store bandwidth and cost related to traditional registers? Of course, you would be storing a lot of garbage, but its a linear and trivially parallel regarding other load and store tasks.