Whenever an artifact falls into the possession of another, I believe it's usually referenced in context such as
"chose another" or
"found itself within the hands of another". This somewhat implies the artifacts are sentient and "choose" their bearer, though this may actually be direct manipulation by the Daedric prince themself. They love that sort of thing, after all.
Honestly, I'm sure that Daedric princes have plenty of different "gifts" to bestow upon those who do their bidding. There's probably plenty of other artifacts, as well as other potential rewards for the summoners, such as forbidden knowledge or a powerful spell. I believe it's more a game limitation than anything - Bethesda originally created artifacts during Arena/Daggerfall when the series was more DnDesque and you could simply see them as "rare treasures".
However, they've remained with the series due to how useful (and undoubtedly iconic) they are. Would you rather waste time developing a bunch of different potential goodies to be distributed among Daedric quests with varying levels of utility or recycle the unanimously-awesome "artifacts"? Actually don't answer that question - I could see realistic jurisdictions for either of these. Point is, it's more of a game limitation than anything else.
If you
really want to look deeply into it however, the Nerevarine prophecies, CHIM, and remarks by Dyus/Jyggalag imply that the main character is indeed "special" and able of controlling their fate. Perhaps that's just it then - it is destiny that brings these invaluable items into our hands as opposed to those of the others. Well, or maybe the Princes (especially ones such as Boethiah and Azura) simply know of your quest and inevitable victory and want to help you out.