>not able to get out of labs even after a century

It got out of labs in a quite spectacular way in the summer of 1945, eighty years ago.

Thought experiment: did we really need quantum mechanics to build an atom bomb? Couldn't we have built one with a model of the atom based on classical particles (with protons leading to a chain reaction)? Is either the quantized or the uncertainty aspect of QM necessary for this?

Most of the science going into the Manhattan Project was experimental measurements and phenomenological models, not fundamental physics at the QM level. There were no usable quantum-mechanical models of nuclear physics at that point.

No; they didn't really need it.

It’s just a coincidence that they employed so many experts in quantum mechanics to do those nothing-to-do-with-quantum-mechanics experimental measurements.

Coincidence. If you wanted to do something with elementary particles, you couldn't possibly ignore quantum physics.

Nucleon orbitals rely a little on Pauli exclusion principle, which you need to add as an ad hoc hypothesis every time in classical physics.

The very idea of matter and energy being quantized into particles and photons is the starting point of “quantum” mechanics.

>Planck discovers the quantum nature of energy in 1900

https://www.pbs.org/wgbh/aso/databank/entries/dp00qu.html

It wasn’t developed into a mechanics until the 1920’s.

>did we really need quantum mechanics to build an atom bomb?

Yes. Nuclear reactions require understanding and modeling of the strong force, you can't understand or even see what protons and neutrons are without understanding the strong force. The mixture of positively charged and neutral particles being stuck together with enormous force which essentially does not exist at all outside of the nucleus of an atom. (there is more than three pounds of force between every pair of protons inside every nucleus with the strong force counteracting the electrostatic force)

You couldn't design a bomb without being able to model the strong force and you couldn't get to that point of investigating the atom without coming up with QM.

You couldn't get the idea of isotopes and enriching U-235 to U-238 or transmuting uranium to plutonium without understanding QM.

Or the circumstances that would lead someone to blindly creating a controlled nuclear reaction without coming up with QM in the process would be pretty absurd.

The idea for the bomb came from the understanding of the strong force. Step one: notice that there's a crazy powerful force keeping positively charged particles stuck together in the nucleus. Step two: the eureka moment of realizing you can "release" that force by causing a chain reaction of fission in heavy elements.