Treating your MVC controllers as your DDD application layer will present a few negative situations.
The biggest one is that your application layer (regarding DDD), is one of the key places where you model your domain/business processes. For example, you might in an application service have a method called:
PayrollService.CalculatePayslips();
This might involve, checking a domain service or external system for the current active employees, it might then need to query another domain service or external system for absences, pension deductions, etc. It will then need to call a domain service (or entity) to do the calculations.
Capturing domain/business logic like this in the MVC controllers would cause an architectural issue, should you want to trigger the task of calculating payslips from elsewhere in the system. Also if you ever wanted to expose this process as a web service, or even from another MVC controller, you would have references going across or up into your presentation layer. Solutions like these "might work", but they will contribute towards your application becoming Spaghetti Code or a Big Ball of Mud (both code smells in an architectural sense). You risk causing circular references and highly coupled code, which increases maintenance costs (both time, money, developer sanity, etc.) in the future.
At the end of the day, software development is a game of trade-offs. Architectural concerns become bigger issues, the bigger your application grows. For a lot of very small CRUD apps, architectural concerns are probably negligible. One of the key goals of DDD is to tackle complexity, so it could be argued that most DDD projects should be of sufficient complexity to be concerned about good enterprise architecture principles.