First, I am curious if you allowed such inanity in 3.5e? Does a bag of holding wrapped around some rocks overcome DR 15/magic?
In every previous edition, monsters required a weapon with sufficient + to hit and damage. In AD&D and 3.0, it was spelled out as +1, +2, etc. In 3.5, /magic DR required a weapon with at least a +1 bonus, and /epic DR required a weapon with at least +6. It would not suffice to hit something with a Bag of Holding or a +3 shield, unless the item was
also enchanted as a +1 or better weapon, which was explicitly allowed in 3.x and not addressed at all in earlier editions.
Second, I believe with regard to 5e you are hanging your hat on the choice of WOTC to word damage resistance as half damage from nonmagical weapons as opposed to saying full damage from magical weapons. You are saying that since they are resistant to nonmagical weapons, they must not be resistant to EVERYTHING else.
The fact that the damage resistance entry uses the term "nonmagical weapon" as opposed to "nonmagical item" implies greatly that the converse, magical weapons (and only magical weapons...not magic items) do full damage.
If you check the current version of the DM's Basic Rules, which I believe reflects current errata and which was changed to better convey the intent of the rules, resistance or immunity to certain weapons has been updated to say that it's resistance to damage of those type from nonmagical
attacks. You can attack someone with an improvised weapon, just as you can attack with a sword.
The previous terminology was changed because it didn't convey the proper intent. Saying that you needed a magical
weapon in order to deal slashing/piercing/bludgeoning damage to a golem was apparently misleading, possibly because some people were stuck on the idea that a "weapon" is some sort of specifically-defined system term rather than the natural language which describes the thing you use to make attacks that deal damage. An improvised weapon is entirely as much of a weapon as anything else, even though it can't be encapsulated in chart form, and there's even a specific rule for improvised weapons
that bear no resemblance to a weapon.