Given the similarities between us and other animals, it should make more sense to have to disprove that they don't feel pain, rather than having to prove that they do, i.e., that they must feel pain should be the default assumption in the absence of data.

Which similarities?

Insects have a much, much simpler nervous system. They don't even have a spinal chord, and they have an exoskeleton.

I think maybe only cnidarians have a simpler (or similarly complex) nervous system.

Pain on a chordate might be comparable to pain in humans, with some exceptions like the Octopus (maybe) but that's about it.

But we don't know that insects absolutely couldn't experience pain, in the same way that we're certain a brick couldn't (unless one is a panpsychist). At least they have a nervous system.

Pain as in stimulus to nerve endings given damage to a limb yes

But pain in humans (or other more complex animals) is more complicated than that

It may be more complicated, but do we know the minimum complexity required of a nervous system to support 'suffering'? If not, surely we are obligated to give even the simplest nervous systems the benefit of the doubt.

No, animals don't perceive the world as we do but it's not stretching things at all to say that they do (have to!) register some of the basic realities of life such as warmth, cold, pain (i.e., 'this is bad - something's not right and needs to be sorted') and absence of pain. The nuts and bolts of this are bound to be similar or identical given that we share a lot of basic biochemistry with all life forms. For example the citric acid cycle (a fundamental engine for energy production) operates together with its associated pathways universally in plants and animals.