Having a per-instance seed allows for things like procedurally generated worlds where the co-ordinates are used to generate a seed, while still allowing a separate per-session random instance to control events. A global value also impacts on thread safety.

As an example, in C++ the classic std::rand() uses a global seed initialised by std::srand(), where as the newer C++ random generators are instance oriented.

It depends on what you're trying to do with what.

If you're only ever going to use a single LCG PRNG, then if you want it to act like a global variable, go ahead and use a global variable as its seed.

If you want to use something more sophisticated than a single 32-bit LCG, like a lagged Fibonacci or a Mersenne Twister PRNG, then a 32-bit initialization vector is insufficient to start with.

If you want to use several different PRNGs in an application, how could a single 32-bit initialization vector ever help you?

If you're relying on a single 32-bit initialization vector in the global namespace to be uninitialized to use as a seed value for any PRNG, you are in for a quality debugging treat.

Initializing an initialization vector in the constructor of a PRNG object makes no sense. You want to pass the initialization vector in to the constructor so it can use it to initialize the PRNG.