You have to know that was on a tiny scale. The reason hydroponics are rarely used today is the expense. While it will admittedly work, more traditional methods also work and cost less per ton of food.
Many things today are done on a small scale... that doesn't mean they cannot be (or couldn't have been) scaled UP.
Traditional methods have destroyed 30% of arable land on Earth over the past 40 years.
While we have been producing enough to feed 10 billion every year (for just over 30 years now), presently used methods are unsustainable and you expend a lot of energy on transporting the food in question whereas we can easily grow it locally in fully automated vertical farms.
Ignoring the fictional notion of 'cost', technologically/resource wise, it was doable some time ago.
Good God, how many kilowatt hours is that going to consume in the process of creating enough food for everyone? Modern farms do use energy of course, pumps and John Deere. But nothing like what you're purposing. Power isn't free, sunlight is though.
You are apparently forgetting that we already have the ability to create structures that are not only energy efficient (even more so if they were made from superior synthetic materials), but can also produce energy (by making the structure walls into solar collectors) and water (using atmospheric water generators).
On top of that, 1.2% of Sahara desert alone can power the planet using concentrated solar power.
Less than 1% of Earth is needed to power the planets projected energy demands of 2050 with CURRENT solar technology.
Tapping into just 1% of Earth's geothermal capacity can provide us with power to last us 4000 years.
And what purpose is served by putting the plants in a 44 story tower? If you were to go with this (again silly) idea, a 44 acre, one story greenhouse building would be far easier to construct and maintain. It could be sealed providing many of the advantages you apparently want, and have natural sunlight part of the time.. Much cheaper than a 44 story building with a one acre footprint.
The 'purpose' (among others) would be to minimize footprint and produce food LOCALLY (eliminating transportation requirements).
A 44 story building would cost well over a 100 million dollars. A one story building with the same floor space, less.
There you go again with the fictional 'cost' notion.
I'm not referring to money, I'm referring to what can be done using proper implementation of science and technology that can give us abundance (more than what we need or want) while reducing our footprint.
Because putting an additional 3 percent of the American workforce on unemployment is a GOOD idea.
Actually, in case you hadn't notices, its already happening.
Its unavoidable, because its much more efficient that human labor (which is slow, requires breaks and is inefficient).
Oh yes... the purpose of using full blown automation (without planned obsolescence and making it with highest possible efficiency we can muster in abundance) is to basically liberate Humans from having to 'work for a living'.
Point is, technology rendered money (as means of exchange) useless decades ago, because we have been producing abundance in virtually every field for just over 100 years now.