I've always felt that Arceus should have been uncatchable but with impossibly high (like all above 200) base stats and a multiple stage boss battle (perhaps 6 randomly selected elemental forms) . It would have made him an interesting final boss who would be genuinely difficult to prepare for.
Um, simply put, not all gods are "the God," of most of todays religions. As in, they are potentially defeat-able, and catch-able. Not completely invincible, not all knowing, not capable of doing everything, etc.
Its not different than killing an Ancient Greek God.
Not all cultures believe in some infallible God. The Greek Gods weren't perfect and were killable. --- "As I was walking up the stairs, I met a man who wasn't there, he wasn't there again today, i wish I wish he'd go away."
If a deity like being feels like travelling with someone, then it will.
Really, I think that's the mentality all the legends are implied to have; running around with a kid fighting strong opponents and seeing new places (particularly if you think about importing and trading in a narrative sense) is fun for them.