Do electrons and protons not want to be near each other?

Wouldn't oppositely charged particles attract each other and if not for the centrifugal force on the revolving electrons, they would get dragged towards the protons and fall into the nucleus?

Yes but this is very improbable even in classical-theoretic models. If the electron moves transversally ("around the center") in pure central Coulomb field of the nucleus, this motion is enough to prevent the fall into the nucleus, because in a central Coulomb field there are stable elliptical orbits like there are for planets orbiting the Sun. If we take into account radiation of the electron and the proton, then these orbits are not stable and the electron can fall on the proton.

But if we then take into account the background radiation as well (due to all other bodies in the universe), there are numerical indications that this can prevent the collapse [1]. The simple explanation is that the external radiation keeps kicking the electron out of the proton vicinity.

[1] Cole D. C., Zou Y.:Quantum Mechanical Ground State of Hydrogen Obtained from Classical Electrodynamics, 2003, https://arxiv.org/abs/quant-ph/0307154

In the standard quantum theoretical model of the hydrogen atom, the electron does not have position and velocity. Instead, it is described by a function $psi$ of coordinates $x,y,z$. This function could get sucked into the proton, if the central field was increasing stronger with decreasing distance than the Coulomb field does. For example, attractive central field that varies as $1/r^4$ is too strong at the singularity and according to the time-dependent Schroedinger equation it will suck the $psi$ function into the singularity.

But for the Coulomb field there are stable solutions where the $psi$ function is finite around the proton in a region with dimensions of magnitude 1e-10 m. This "noncollapse" is due to the Schroedinger equation containing quadratic term in momentum.

So, the mechanism varies in different models, but they all are capable to account for the fact that although electron is attracted, it does not fall on the proton too frequently.

An electron is associated with a wave. The amplitude of the wave at any point determines the probability that it will react with something else at that point. Electron orbitals in an atom are resonant 3D standing wave patterns bounded by the electric field from the nucleus. These patterns are much larger than the nucleus, and the probability of their interacting with something in the nucleus is quite small.

You are correct, the planetary model of the atom would not work, because the orbiting electron would accelerate and lose energy and fall into the nucleus. This is one of the very reasons QM was invented.

One of the reasons for "inventing" quantum mechanics was exactly this conundrum.

Why don't electrons crash into the nuclei they "orbit"?

By the way, with certain probabilities, electrons do exist inside the nucleus, and sometimes even "crash" into it, we call it electron capture.

https://en.wikipedia.org/wiki/Electron_capture

Now if you accept that the underlying nature of the universe is quantum mechanical, and electrons exist in orbitals (not orbits), and the wavefunction describes the probabilities of the electron existing around the nucleus, then you continue your way towards the Heisenberg Uncertainty Principle.

https://en.wikipedia.org/wiki/Uncertainty_principle

Then you will see that the reason electrons exist around the nucleus in stable orbits is rooted deep in QM because:

1. the EM force is attracting the electron and the proton

2. the HUP keeps the electron from existing in a too small region of space, thus balancing the EM force (the reason why electrons exist in quantized stable orbitals is more complicated and needs deeper QM)

And there you have it, the existence of a beautiful balance and an explanation why QM is the dominant description of the atomic level.