So.
The D20 wiki for the mage hand says it cannot activate magical items. I presume this is for things that require some kind of active magical channeling, rather than, you know "Push a button".
I say that, because an immovable rod is a magical item, that is activated by -- you guessed it-- PUSHING A BUTTON.
Now:
The Mage Hand can only carry 10 lbs, and can only move 30 feet away from its user before being dispelled.
https://roll20.net/compendium/dnd5e/Mage%20Hand#contentAn immovable rod weighs just a few pounds, and is activated by depressing the button socketed into the end of it.
https://roll20.net/compendium/dnd5e/Immovable%20Rod#contentClever use of a good length of rope, mage hands, and immovable rods, could be used to make a "very sluggish" "Magic carpet".
Imagine:
The rope is tied to the immovable rods using timber hitch knots.
https://www.netknots.com/rope_knots/timber-hitchBetween the rods, the rope is woven into something resembling a cargo net.
Riders sit in the netting.
At any given point, the weight of the riders is sustained by the immovable rods, NOT the mage hands. The apparatus moves "sluglike", in that it incrementally moves each rod forward slightly by deactivating it, tugging on the netting so that it moves forward/upward/whatever, then activating it again, in a rhythmic, repetitious pattern.
Since each rod can carry up to 8000lbs of dead weight, having such a contraption made from several rods, an entire party, and their loot, could be "slugged" along, even over a very large expansive crevasse. That you can move a mage hand up to 30ft at a whack, even with its 10lb restriction (as long as the weight of the netting itself tied to it does not exceed 8lbs) the combined weight of the net and rod at each moment of movement will be within its limitations, and cloud potentially move quite quickly.
Being a net, the party could look down through it, and even shoot arrows down through it, without much issue. Being sufficiently high up (such as in open terrain), would make them vulnerable only to flyers and mage fire. (and if they are using fire proof rope, and have suitable tower shields to sit on, even that might not be a problem.)
Sorry, I imagine silly things like this when I read about nonsense items like these.