It’s not that no one cares. We just want one that’s under 20K, has more than 45 minutes flight time, isn’t loud or bulky, and is extremely safe.
The main defining features of a Part 103 ultralight are empty weight (< 254 lbs, including battery but not including up to 5 gallons of fuel, and with additional credits for parachutes and floats), minimum flight speed (stall speed for a fixed wing aircraft) of <= 24 kts or calculated equivalent (see AC 103-7), and maximum horizontal flight speed of 55 kts (with electronic or other artificial restriction of speed being acceptable).
Many of the "jetpacks" and other ultralight VTOL ideas being explored right now easily fit within Part 103, so in the US these certainly can fly, at least for very limited recreational usage.
Now, flying them over other people's property or over a city is, and should be, another story.
It's not "one of the most dreamed of forms of flight – jetpacks" if you can't fly around town.
For jetpacks there is an additional huge problem with safety flying over inhabited areas. Unless the jetpacks are meticulously maintained and inspected, we would see people falling out of the sky on the daily. Taking the maintenance state of most cars as an example, it seems safe to state that it would be infeasible to expect the general population to keep their jetpacks in an acceptable state.
No person may operate an ultralight vehicle over any congested area of a city, town, or settlement, or over any open air assembly of persons.
I don't think the reason for this deregulation is that the FAA doesn't care if you only kill yourself, but rather that the number of people interested in doing this is and was in practice incredibly small. Yes, anyone can go buy a paramotor for $10,000 and probably figure out how to operate it just well enough to be able to kill themselves, but in practice this is extremely rare.
You can be sure that if it somehow became wildly popular for people to buy these things and it was causing lots of problems, the regulations would change. The exact thing happened with the massive popularity of "drones," which were similarly deregulated because the usage of RC aircraft had also been limited to a small number of RC clubs around the country.
That's enough to reach critical mass of many fissile elements. I wonder if it would be possible to build a miniature nuclear rocket with enough thrust to lift a human. The weight budget probably isn't enough to include enough shielding.
These are of course, impossibly contradictory requirements for a jet-engine device.
That's a paramotor.
Still, not enough people care.
A bored person in a car with the radio on, stuck in traffic, in 1970, imagines the freedom, the sheer dopamine rush of escaping by soaring away on a full-throttle personal jetpack, like "the right stuff" had finally trickled down.
A bored person in a chair with a podcast on, stuck at home, in 2021, refreshing their social media. Watches a jetpack video on TikTok. Shrugs and moves on to the next distraction.