The $p$ orbitals, for example, have a nodal plane where the nucleus is, which means the electron density is zero there.

An orbital doesn't represent a path the electrons take when moving. An orbital is a region of probability. To make things clear and definite, when we draw an orbital we only draw the region where 95% (for example) of the probability lies. The fact that the $p$ orbitals have a nodal plane simply means that the probability of finding an electron on that plane vanishes.

A positivist would thus consider an electron's trajectory around a nucleus nonsensical, since by the uncertainty principle, we can never measure it.

The use of orbitals is for visualizing electron density - where can the electron be, most of the time? It's a very useful way of interpreting phenomena such as chemical reactivity (think of SN₂) or stability (think of benzene's $p$ orbitals).

The $\mathrm{p}$ orbitals, for example, have a nodal plane where the nucleus is, which means the electron density is zero there.

An orbital doesn't represent a path the electrons take when moving. An orbital is a region of probability. To make things clear and definite, when we draw an orbital we only draw the region where 95% (for example) of the probability lies. The fact that the $\mathrm{p}$ orbitals have a nodal plane simply means that the probability of finding an electron on that plane vanishes.

A positivist would thus consider an electron's trajectory around a nucleus nonsensical, since by the uncertainty principle, we can never measure it.

The use of orbitals is for visualizing electron density - where can the electron be, most of the time? It's a very useful way of interpreting phenomena such as chemical reactivity (think of $\mathrm{S_N2}$) or stability (think of benzene's $\mathrm{p}$ orbitals).