Absolutely nothing wrong with it, IMO. The canned "this isn't what inheritance is for" response doesn't apply here. In fact, if anything, this is what inheritance is for - you want all child controllers to inherit this behavior from the parent. The fact that you're only reusing one line of code is your business and does not affect the validity of using inheritance here.
I would go for it, primarily because it will make it harder for developers and maintainers to forget it. If every controller has to extend your base controller, it will look obvious when you open a non-inherited one. It is MUCH less obvious when you look at a class without a constructor, especially if your team doesn't always put constructors at the same spot.
As a teeny side benefit, it's a bit less typing than calling out from the constructor, at least in the cases where you wouldn't otherwise need an explicit constructor.
There is no counter argument I can see, unless you have some edge case where the IE header is undesirable (maybe a non-html content type?). It also does not preclude you from using additional layers of inheritance for your controllers, since if you needed a couple controllers to inherit from a "different" base class, you'd just make that new base class inherit from your main base controller.