Type-inference is needed in C++ (and is already part of the next standard, you can enable the auto keyword with gnu gcc already). But it's needed for entirely different purposes than what scripting languages use it for: it's a feature for writing better templates.

It's confusing because there are two types of type-inference (run-time and compile-time). You do lose performance with run-time type-inference, which is what most interpreted languages use. C++ already has compile-time type-inference in the form of templates. They are...complex. But they're also faster than anything similar. There's a reason that C++'s sort is usually faster than C's qsort for complex types.

C++ doesn't have run-time type-inference and probably won't. The performance loss is too big to build it into the language everywhere, and unless you do that it's pretty pointless. You can tack it on with boost::any or RTTI, for example, but you'll generally find that it's not the correct decision from an engineering standpoint. Scripting languages have run-time type-inference built in everywhere -- but they do it at the cost of performance.

Now, as far as the problems of C++'s dependence on C...well, you're right. It's a feature of C++'s history. If someone could come along and invest the millions of man hours required in making a performance-critical high-level language without the C-baggage (and then market it!), it would be a great thing. But that's a pipe dream. The best we're going to do on that front is Java.