I think it matters because it informs how I think of the Church on earth and the promises of Christ and that is something that I do have some measure of control over. I should want my understanding to conform to how the Church thinks, which naturally will give rise to many important questions such as the one we are now discussing.
Is Canon Law good for learning/teaching how the Lawgiver thinks?
What does the law say about these things on heresy/loss of office?
What do the commentators say on those canons?
I guess I just figured that there must be a certain way of viewing the situation that would be - at one end, "more/most pleasing to God" and at the other end could be crass ignorance, negligence, or even implicitly heretical - and then there is everything in-between.
You may think one way, I another, we may both be permitted to do so using Catholic sources to support our position, but that doesn't equate that both positions would be equally pleasing to God. Is religious life "better" than marriage? Are following the counsels and precepts better than just follow the precepts? Is it better to walk 1 mile along or 2? Ya feel me?
Do you come at your faith like this;
1) "I can believe x because, it is no sin - I am permitted to believe it - so there."
OR
2) "I can believe x or y or z, - it is no sin - which one do I think is more pleasing to God?"
Will said choice be "more pleasing to God"? Not necessarily, but the intention and the motivation behind it are better than just a straight #1. Go for #2.
Hopefully that helps, as I would assume you did not intend to straw man St. Bellermine et nal, with your, "obsession with proving" bit.