Yes but making new classes map to default is what a default clause already does (which is basically what a base case in an abstract base class does with normal inheritance).

What I want is to make a new type added mean the code won't compile until it is explicitly handled in all pattern matches that do not have a default clause. Basically what I'm saying is that this:

   bool HandlePayment(PaymentMethod pm) {
      switch(pm) {
         case Invoice(addr):
              SendInvoice(addr); 
              return true;
         case CreditCard(ccdetails)
              return PrcessCreditcard(ccdetails);
         default:
              // What?
      }
   }

Would be a lot better if it didn't require the default, and the compiler could detect the error that occurs when someone adds a new case (BitCoin) to the types of payment method. Inheritance and abstract baseclass for the processing means that you'd do this

   bool HandlePayment(PaymentMethod pm)
   {
      return pm.Process(order);  // sends an invoice, charges credit card etc
   }

   and you simply have 

   abstract class PaymentMethod { abstract bool Process(order); }
   class CreditCard : PaymentMethod {  ... }
   class Invoice : PaymentMethod {  ... }

And this is of course the regular way of writing OO, but I find it unnatural and cumbersome in many cases. It's hard to define concise descriptions of what types are actually available, and you have to write a ton of boilerplate to ensure a closed hierarchy and complete matching in all scenarios where you can't enclose the logic inside each type.