In Dungeon Master's Guide, on page 141 it says thay when casting a spell from a magical item that allows one to do so, eg. a wand, the caster must concentrate on the spell if the spell requires concentration when cast normally.
However, there is no rule here saying thay the user needs to retain control of the item to maintain concentration on the spell. Does this mean a different character could plausibly take the item in question and cast a new instance of the spell from it without having to break the first instance? Is there another rule I've overlooked that would prevent this kind of use of wands and other magical objects?
If a wand doesn't requirement attunement, it can be passed around from player to player much in the same way you can hand out potions from one player to another.
However, there are ZERO wands in the DMG that have combat-focused concentration spells that do not requirement attunement.
As you said, Wand of Magic Detection is the outlier here, and Detect Magic is fairly innocuous (doesn't help with finding invisible creatures, for instance.)