Is this a possible explanation as to why sigma bonds are stronger than pi bonds?
This is a very short answer and it might as well have just been a comment. It is probably also tempting in it's simplicity. For starters, let's assume, that nuclei are point charges.

When two atoms form bonds, all the electrons experience the attractive force of the nuclei, of both of them. This is independent of the type of orbital the electrons occupy.

In a &sigma; orbital, the path of maximum electron density is between the nuclei. It is also where the electronic field of the nuclei is strongest. For a &pi; orbital the situation is different.

Let's take a step back and consider an atom. The s orbital is spherical symmetric. The maximum electron density is (formally) in the nucleus. For the p orbital, there is a node at the nucleus. The maximum electron density is further away from the opposite charge, causing attraction to be lower. The energy of the orbital will be higher.

Similarly we can see that for &pi; orbitals. The node of these kind of orbitals is exactly where the field of the nuclei is strongest. Hence the attraction is lowered, the energy raised, because the maximum electronic density is further away from the nuclei.

In very short terms: In &sigma; orbitals the maximum electron density is on the bonding axis, while in &pi; (and &delta;) orbitals it is off the bonding axis.