In Integrate-and-fire models, why can we assume spike arrivals to be random?
Assuming random spike arrivals is just a convention that is chosen, not an assumption of some natural system. It's not a property of integrate-and-fire models. Probably whoever chose this convention did so for some demonstration (teaching) purposes. It may also be chosen to model "neural noise" which is a shortcut for "all the other stuff going on in the brain besides that which we are studying". In that context, it's common to model the effect of a consistent incoming signal on a random background.

An equivalent might be to see how an electronic filter would respond to either an impulse or to white noise: you could learn something about the filter (such as its ability to attenuate certain frequencies, or a certain response pattern to an impulse) by looking at either of those responses.

Similarly, by feeding noisy/random input to a integrate-and-fire neuron, you can find how changing parameters of your model neuron changes its output properties.