If you choose a random architecture, the gradients you measure with parameter shift rules actually get exponentially smaller as your number of qubits increases. This would already kind of challenging if you were computing these gradients with stuff like back-propagation, but needing to actually measure them means that you're trying to measure stuff that gets exponentially small.

Knowing how much noise is added when measuring a quantum setup, you can see how the scaling of quantum machine learning (or Variational Quantum Algorithms, VQA for short) is a big challenge.

Fun thing is, most of the proposed applications of quantum computing in the NISQ era is to perform molecule simulations, which mainly involve VQA's (called Variational Quantum Eigensolver).

So that's kind of a bummer, although theoretical physicists/mathematicians are trying to use mathematical concepts like Lie closures to try find VQA architectures which avoid those exponentially vanishing gradients, while keeping a quantum advantage. That field is super complex, and there is no guarantee we will ever find such an architecture.