I'd be extremely surprised if the "proficiencies" granted by background shared any common ground with things like weapon and armor proficiencies. There isn't going to be any overlap between backgrounds and feats. They know better than to make that mistake. If they don't, we'll tell them when they make it, and they'll fix it.
One of the things that demonstrates different D&D interpretation styles is how people view character customization. See, I look at it and see:
1. Start with a race (from a half dozen or more choices), ability scores (with a lot of customization), background (of probably dozens of choices), and alignment (if desired)
2. Add an adventuring class (of which you will have around a dozen or more choices), and equip your character as desired
3. Add a subclass (of which you will have multiple choices for each class), either immediately or in the first few levels
4. Then add a feat/specialty (of which you will have many choices) at about level 4 or 5
5. Multiclass if you want to
6. Add additional feats as you level up
And I think, "how is that not enough character customization?"
I just don't see "I don't want to be like every other fighter" as a valid criticism, since it is rarely accurate. It simply sounds more compelling than saying, "I don't want to be like every other Str 12, Dex 16, Con 12, Int 13, Wis 15, Cha 10, chaotic good, wood elf, giant killer ranger with a priest background who wields shortswords, a longbow, and throwing daggers, and prefers studded leather armor. And 4-6 highly flavorful suites of special features that I can select isn't going to cut it." Really? This is a class-based system. There is going to be plenty of customization for a class-based system. Any more customization and you hardly have a class-based system.
I love skill-based systems. D&D is the only game that I actually like a class-based system in. So I find arguments that amount to saying, "that's too much like a class-based system" rather foreign to my preferences.
Play what you like, it just makes me shake my head like a boat was missed somewhere.