If you want protons, you just strip the electron off a Hydrogen atom, at the cost of 13 eV or so. No need for nuclear physics.
If you want neutrons, (and a lot of experiments do) you have to use nuclear physics.
Lighter nuclei have a lower ratio of neutrons/protons, therefore fission tends to produce extra, free neutrons.
The question is how to induce fission. Either by neutrons, which is easy because the neutron has no charge (but you need a source of neutrons to do this), or by spallation with protons.
Protons are more difficult to use because of their charge. It takes a lot of energy to get the proton close enough to the (positively charged) target nucleus before any nuclear reaction can happen.