Not too familiar with this specific work, but it's not so uncommon in math that proofs are first found using some very large inputs that are then progressively simplified in further work. One prominent example would be prime gaps: in 2013 someone proved that there are infinitely many primes that are at most ~70 million apart, and in the following years that gap has successively dropped to 246 iirc (the goal remains getting it down to 2, of course). And there are some famous examples of far larger numbers, some too large to meaningfully represent in our physical universe, that have been used in proofs and then rendered obsolete by later work (eg Graham's number, Skewes' number).
So (again, without knowing much about the problem at hand), the answer to your question might be that the simplest possible examples are much simpler anyway.
So (again, without knowing much about the problem at hand), the answer to your question might be that the simplest possible examples are much simpler anyway.