Unfortunately, 5e is fine with dead feats. The same thing happens if you choose Dwarf, which has Axe/Hammer Proficiency, and Fighter, which includes it in Martial Weapon Proficiency. I've never liked that. I think if you are predisposed to already be "partway there" from your background or race, you should get a little boost when you take the class.
This would be the most ridiculous thing for them to be strict about. Holy Heck, they are going to give you access to all sorts of spells you haven't earned (and they do warn you about duplicate spells so you can pick different ones), but skills are where they are going to decide to make it difficult for noobs?
That's some lame prioritization.
Hopefully multi-classing into rogue/bard/ranger isn't going to be a forced skill, too.