Setting aside whether such seats are actively hazardous to passengers for anything more than a short-haul flight -- they almost certainly are -- we can fairly easily rule out the possibility based solely on one of the more important airline test criteria: evacuation time.
For all commercial passenger airliners, the primary limiting factor for economy seating is how to get everyone out of the airplane in an emergency situation within the stipulated time, in ideal circumstances. In the USA, that time is 90 seconds, based on research that the inferno post-crash due to ruptured fuel tanks would only allow the plane to remain intact for about two minutes. From that article, the largest passenger jet in the world -- the Airbus A380 -- could evacuate 873 people through 16 doors on two dual-aisle decks. A typical short-haul, single-aisle Boeing 737 has only six doors and carries a maximum of 230 passengers with the still-being-certified 737 MAX 10 variant.
The benefit of having more doors and more aisles must not be understated, but even then, another limiting factor is takeoff weight. Using the 737 MAX 10 as an example, the difference between its empty weight and maximum takeoff weight is some 40,000 pounds. But 230 people already accounts for around 20,000 pounds, so the aircraft already cannot be fully loaded with its full 44,000 pound fuel capacity. Packing more people into this aircraft would steal even more capacity and leave the aircraft unable to support transcontinental USA flights.
But supposing that was overcome, and flights with so-called standing seats were only about 2 hours long or so, the problem would then be with seat durability during a crash scenario. Jet airlines seats are designed to absorb energy, since excessive G-forces would kill a human well before any fire might get to them. A seat which relies on human legs for vertical support would be unable to adequately absorb downward forces from a hard touchdown, nor from forces from the jet hitting an obstacle ahead or being rammed from behind. These two directions are what humans are best able to cope with, and a standing seat steals these benefits away.
Thus, a seat that complies with energy absorption requirements would be at least as equally thick as existing seatbacks, and would probably be thicker or heavier, further reducing available payload.
The only conceivable cabin configuration would be one where economy class uses so-called standing seats, in order to free up room ahead for business or first-class seats, staying within the existing seat limits for existing aircraft. However, the time to board such an aircraft would be noticeably slower than with a conventional seat aircraft, so at some point, such an airliner would need to consider whether a stopped aircraft loading passengers is better value than an aircraft which can be quickly turned around for another flight segment. The savings of even 10 minutes per flight can make the difference between a low-cost carrier being profitable or carrying losses every year.
All of these factors point to a technical inability to squeeze more passengers into less space. And remember that there's no free lunch: a "standing" passenger frees up space between rows, but requires more height at each seat. At least from my experience, one cannot stand up in a conventional seat, without hitting the ceiling. How would a typical 5 ft 9 in (175 cm) American be able to use a "standing" seat safely?
It would also eliminate under-seat bags to anything except maybe a clutch handbag, and then the quandary of where the extra people's carry-on luggage would go. For wide body jets, it would actually be more reasonable to create an additional deck by repurposing the cargo hold, but such provisions are akin to building a new aircraft variant outright. Nevermind that passenger aircraft actually make a decent amount of revenue from cargo/freight carriage.
I personally discount the possibility of "standing" seats deployed on existing and proposed aircraft, so it would be at least 10-20 years before we even see such a thing for future revenue passenger aircraft.