Li Shenron
Legend
My solution is that +N weapons/Armor exist, but aren't magical -- they're just mundane items crafted with exceptional skill or using rare/special materials. Magic provides special effects. So you can have a +N weapon without special effects (masterwork but mundane), or a magical weapon with special effects but no +N, or a +N magical item with special effects.
This would have been great in 3e, to have masterwork bonuses replace magic bonuses. In 5e however they have to deal with bounded accuracy so the range of bonuses will need to be smaller, but I like your idea.
There always needs to be a baseline. 3e assumed the baseline was X magic knowing that people could still choose to have have <X magic (and make the game harder) or >X magic (and make the game easier).
Yes. Yes it does mean that a campaign where everyone uses magic weapons everyone is doing more damage and doing better. Because it is above the baseline. Just like awarding more magic than was assumed by 3e.
Yes, but the baseline doesn't have to be "everybody with a magic weapon has +1 to hit".
The baseline could be "everybody with a magic weapon has 1 additional special ability".
This way, there is less impact to bounded accuracy. The baseline is not a "vertical bias" but a "horizontal bias". It means there is much less to worry about re-balancing monsters between groups using magic weapons and groups not using them.
As I said, notice that the same used to be the baseline for armors "everybody with a magic armor has +1 AC", but in 5e this is gone, it's not the baseline anymore (only a few armor give that), despite what it used to be in previous editions... so why couldn't it also be the case for magic weapons?