Aside from what an entirely different property in an entirely different medium has to do with Battlefield, Inglorious Basterds was a mix of typical Tarantino homages to decades of cinema, and meta satire, the whole Nazi premiere basically being a mirror of the audiences watching Inglorious Basterds. We cheer on the violence against the Nazis the same as the Nazis cheering on the violence against the Allies. And probably some alternate history across the entire film for fun (historical realism was never part of it's appeal or marketing).
So the question becomes about what BFV is supposed to be. Is it supposed to be the latest and greatest in a successful franchise going back 16 years, or is it supposed to be satire and using WWII as some kind of allegory for modern times? Even aside from what EA/DICE want to do, what is the most likely ideal from existing fans of the franchise, which is the core demographic of any game that is built on an existing brand (otherwise, use a new brand)?
As many have said, if they wanted satire and meta, they could've made a Bad Company 3, and it would've been more fitting. There is nothing outside the BC series that had any such approach.