Why do ionisation energies have a general increase across periods?

Ionisation energy is the energy required for one mole of gaseous atoms to lose one mole of electrons, hence forming one mole of gaseous ions.The ionisation energies for elements increases across the period because as you move along the group, nuclear charge increases (as atomic number increases) which means that the atoms become smaller- due to the greater attraction between the nucleus and electrons. This means more energy is required to remove an electron, hence meaning the value for the ionisation energy is larger.Taking Sodium --> Argon as an example: as with other periods, this one demonstrates the general increase trend however there are dips between Mg and Al, and P and S. The dip between Mg and Al is due to the outer electron being in different orbitals. In Mg, the outer electron is in the 2s orbital whereas in Al it is in the 2p orbital- the 2p orbital is at a higher energy so the electron is slightly easier to remove, hence having a slightly lower ionisation energy. In P, the outer electron is unpaired, whereas in S the electron is paired- this means in S the electron repels the other (opposite spin repulsion). This repulsion means that the outer electron is easier to remove, so S has a lower ionisation energy.