(If the weight is a great concern, and it is, and capsules are too heavy — hammocks can also be an option).
1) The aisle has to be a set width, so you cant stack cabins across the plane.
2) Passengers need to seated and have a seat belt on upon take off and landing.
I think theres another about being able to be belted in if turbulence happens, and be inspectable by attendants. In short, its not as easy as one may think, and its these regulations which complicate things.
The way I picture it is replacing seats as they are currently laid out in e.g. a 747 - 3 seats become stacked capsules -> aisle -> 3/4 seats become stacked capsules -> aisle -> 3 seats become stacked capsule. I don't deny that getting into these capsules would be awkward for people with limited mobility, but I do imagine it is within the realms of possibility while meeting safety regulations.
In order to stack hammocks or racks three-high, transversely to the fuselage axis, as I suspect you intend, you need both a large amount of vertical space - eight or nine feet, minimum - and roughly a second row's worth of space between racks, in order for people to get into and out of them. The former requirement can be reduced at the cost of squeezing people unpleasantly together and potentially dismaying claustrophobes; the latter requirement can be eliminated at the same cost, plus that of exclusively end-on entry to and exit from the rack, two-thirds of the time via a ladder.
At this point the only customers you've got left are those fit enough to be physically able to use your service, and also unconcerned about being cheek by jowl with at least two strangers - or, if the racks have sidewalls, unconcerned about spending however many hours in a box too small to sit up in. A lounge might alleviate that concern, but what about the others? And where will people put their shoes? (Do you wear yours into bed?)
The alternative is to compromise space efficiency for comfort, and a lot of airlines already do substantially that with A380s and individual sleeper pods.
Hammocks with seatbelts!?
Going to the restroom might prove to be somewhat challenging, though...
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² last time I flew with them was awful, worst legroom I've ever encountered.
Properly sleeping on a flight, on the other hand, feels like luxury.