This isn't a trade-off from adopting GDDR6. They could have had extra 4GB with the current 10-channel arrangement, simply by using 16Gb chips on all channels.
It would also prevent the memory contention issues the platform is apparently having, as all memory would be accessed at the same 560GB/s bandwidth.
Not getting 20GB GDDR6 was a cost decision, not an architectural limitation. I doubt it's a supply limitation considering the Series S and the PS5 are using plenty of 16Gb chips.
Wait, you say it's not a trade-off, and then you give evidence that it is a trade-off.
As I pointed out and as MS has hinted at. The trade-off was between speed, cost, and capacity.
Cost includes increasing complexity (thus cost) of PCB layout and signal integrity as well as memory capacity.
They could have simplified it by having fewer channels as with the PS5, but at the cost of either slower memory performance or greatly increased cost at using premium high speed grade chips that were not yet in mass production.
They could have had a memory pool with uniform speed. But with the channels they decided on, that would have meant either 10 GB (too little) or 20 GB (too costly) with the memory speed grade that they went with. If they used cheaper and thus slower memory chips, then they could have save money on the chips but then the solution would be too slow.
Trade-offs are all about finding the best balance given the limitations of cost, product availability, time for implementation, limits of technology, etc.
Both the PS5 and XBS-X/S are exercises in trade-offs given these and potentially other factors.
You can't say there is no trade-off and then point out that something was limited due to it's cost. True everything (well, outside of products targeting the market where money doesn't matter) is limited by cost. But within that limitation, you decide what you want to "trade-off" in order to find the best balance for the product you are making.
PS5 traded off lower maximum memory speed in order to lower complexity of implementation. XBS traded off low complexity of implementation in order to attain a higher maximum memory speed. Each was governed by how their overall system was architected and how each felt they could best achieve performance given the cost (money) cap that each were given.
Regards,
SB