Take a look at what even the proposer is saying wouldn't be allowed in:

 (1) new and delete.  There's no way to pass GFP_* flags in.

 (2) Constructors and destructors.  Nests of implicit code makes the code less
     obvious, and the replacement of static initialisation with constructor
     calls would make the code size larger.

 (3) Exceptions and RTTI.  RTTI would bulk the kernel up too much and
     exception handling is limited without it, and since destructors are not
     allowed, you still have to manually clean up after an error.

 (4) Operator overloading (except in special cases).

 (5) Function overloading (except in special inline cases).

 (6) STL (though some type trait bits are needed to replace __builtins that
     don't exist in g++).

 (7) 'class', 'private', 'namespace'.

 (8) 'virtual'.  Don't want virtual base classes, though virtual function
     tables might make operations tables more efficient.

C++ without class, constructors, destructors, most overloading and the STL? Wow.