The importance of knowing that charges only occur in nature as integral multiples
The simplest thing to deduce is that charge, when observed under the conditions of the experiment, only comes in 'packets' of 1e. The simplest way to ensure that is that there are 'particles', each having an integral charge.

This is the simplest deduction to make. From here, it would be total nonsense to suppose that charge comes in smaller packets, like e/2, or e/3.

That's why it comes as a surprise to most people when learning about quarks, the components of nuclear particles, that they do have a charge in units of e/3. You don't observe quarks under the conditions of Millikan's oil drop experiment. In fact you don't observe quarks directly at all, but that's a different question.