Why isn't absolutely necessary to plug the grounding probe into the GFCI?
It isn't necessary, but it's recommended. A circuit breaker lets 15 amps flow through the circuit, it doesn't care where it is going. A GFCI monitors what comes out of the power and what returns through the neutral. If they aren't equal, it shuts the circuit down in milliseconds. In a perfect world, nothing should be going through the ground. That's why you should have a GFCI, the ground probe may be working, but if it is a small voltage leak (like a cracked pump housing) the breaker won't detect it. The GFCI will.