Meeting requests are the one type of request which has a natural time component. "Find me some headphones" doesn't have an inherent time component, it has a task completion goal. So, it doesn't make sense for it to auto-expire based on time. Dealing with closing/deleting email based on these fuzzy task completion goals cannot currently be automated, and you'd never want to delete the record of completed tasks, either.
For more complex transactional issues where some parties may be using email, there's ticketing/CRM. Once an issue is resolved, you close the ticket, which may log somewhere else. Generally these systems are more one-sided, where an individual interacts with an organization, and there isn't always much visibility into the ticketing state from the outside.