How does defining God a certain way lead to the idea that God must exist? That doesn't work for any other definitions. A lot is being packed into the words "greatest" and "better".
Premise 1: I define "Foo" to refer to the "blorgest" possible thing: a real situation where I'm the richest person alive.
Premise 2: A real "Foo" would be even "blorger" than a hypothetical "Foo".
We can imagine a hypothetical Foo, but a real Foo is blorger than an imaginary Foo, so if you accept the existence of hypothetical Foos, you also accept the even blorger real Foo. QED I'm the richest person alive.
The ability to conceive of something more extreme in some quality than what exists in reality can't obligate reality to change at all.
Premise 1: I define "Foo" to refer to the "blorgest" possible thing: a real situation where I'm the richest person alive.
Premise 2: A real "Foo" would be even "blorger" than a hypothetical "Foo".
We can imagine a hypothetical Foo, but a real Foo is blorger than an imaginary Foo, so if you accept the existence of hypothetical Foos, you also accept the even blorger real Foo. QED I'm the richest person alive.
The ability to conceive of something more extreme in some quality than what exists in reality can't obligate reality to change at all.