I disagree with your conclusion in a slight, but important manner. You write “it is shown, mathematically, that this relic does, in fact, increase your chance of getting better gear.”
A minute increase is an increase but not necessarily a significant one. If you look at the tables provided by @slif_one from the wiki you can see that the percentages barely change whether the relic is applied or not, with anything above uncommon either not changing or changing by such tiny amounts that it’s not significant.
You clearly like running the Vault Hunters relic and so by all means keep running it, it’s not hurting anything