The ring must be attuned, and you can only attune three items at one time. So if your non-caster wants to use this ring for shenanigans various and sundry, he can have the ring plus a magic weapon and a suit of armor (for example), and that's it. No ring on the other hand, no magic boots, etc.
Also remember that attunement takes some time to execute (an entire short rest, to be precise). Trading off the ring among party members may not always be a practical option.
And finally, the person casting the spell to be stored is giving up precious resources until the next rest. That's all well and good before the adventure begins, but it becomes more and more burdensome if you have a campaign where you are using a lot of spells with little downtime. This is particularly true of the warlock-only spell hex.