Why are there things that the mage hand can't reach? This makes zero sense unless what you're trying to reach is more than 30 feet from the caster. The hand floats! Let it do what it is meant to do. Honestly I would be happy for them to remove the offensive abilities like unarmed strike and grapple as the spell was never intended for those purposes. It can literally only pick up things that weigh 10lbs or less RAW. That means it has less than a 1 STR. It specifies in the spell description that it can't attack or activate magic items but any "interact with object" action should be viable including containers, etc.
+1 Mage Hand should be useful for interacting with objects, especially distant ones.
This is somewhat related to the Fly issue in BG3, but not exactly the same. With a flying character, players would expect to be able to manually move their characters in 3D which is a hardish thing to program. But Mage Hand? Not really. If it needs to elevate to pick up an item, the game can take care of that by moving the Mage Hand in a direct line (if possible) to the item and then back. I would guess that this is much easier to code than full 3D maneuverability by the player. Basically turn it into a slow projectile, pick up item, bring mage hand back, and deposit item in character's inventory.
You know what, Larian can even leave in its ability to attack/shove at this point. -1 STR is a -5 modifier, so sure it can make an attack/shove with a -5 bonus, at the cost of your Action of course.