It's not entirely clear whether you are talking about the semantics or the pragmatics here. Your question reads more about semantics, but in the comments you say you are asking about pragmatics. I'm going to answer about both.
Semantics
- Pros: simplicity. Why have two concepts when one will do?
- Cons: none.
Pragmatics
- Pros: simplicity. Again.
- Cons: Performance.
The Real World
The way this is used in the real world is that you have pure object-oriented languages whose implementations use primitives without ever exposing them to the programmer. So, the only people who need to deal with the complexities of having two different "things" (objects and non-object primitives) are the compiler/interpreter implementors. Language users simply use objects.
So, in other words, use semantics without primitives, but implement them with primitives. YARV, Rubinius, MRuby, MacRuby, pretty much all Lisp and Smalltalk (and derivatives such as Self and Newspeak) implementations, some ECMAScript implementations, and probably many others do this.
The techniques for doing this have been known since (at least) the 80s. Like many other useful things, the designers of the Java platform seem to have forgotten them when they designed the Java platform, and are now fighting a decades long uphill battle against backwards compatibility constraints to remove primitives again. (They are rumored to be gone by Java 10, but then again, this rumor has been going around for 15 years now.)