I agree with where you are going with this and do think there needs to be a rework, but that being said, let's look at some math. If you lose a round in Kyber, you get 200 crystal vs 150 in Aurodium (extra 50 for winning as well). So using your logic, that will be 9 battles per championship which nets you an extra 450 crystals in Kyber. If you purposefully lose to stay in Aurodium, then you won't be getting 2-4th all 3 times. I'm sure you can sneak in a 5-7th in Kyber once as well. So, say you get 2-4th two times and a 5-7th 1 time in Aurodium, that's 1250. Now Kyber 8th twice and 5-7th once is 600. Add your extra Kyber crystals for losses and your at 1050. Add in the extra 230 you get at Kyber 5 instead of Aurodium 1 championship and now you're at 1280. Crystal wise, you're about even, but you are still losing out on zetas and some other things.
In my opinion, I believe this is why some players purposefully tank a week in GAC, as you have stated, so that they can get some of the 2-4th or even 1st rewards, rather than taking 8th or 5-7th in the next league up. There should be some guarantees for taking 5-7th or even 8th in the upper tiers in GAC. You fought to get up there, so 8th place in Kyber 5 should be more lucrative than anything in Aurodium. Maybe CG can just up the crystals per loss to like 250. That would net an extra 500 just for being at the bottom of K5 compared to A1.