If everyone is not storing, then those who store will have an information advantage.
In XMR's present case, full nodes store everything.
In XMR's future case, full nodes store everything and SPV-style nodes store just a cache of what they need.
In BBR's present case, "somebody" stores everything and full nodes do not store rings.
In BBR's future case, "somebody" stores everything, full nodes do not store rings and SPV-style nodes are still required.
Do you see where I'm going with this?
No. Could you be more explicit?
In BBR's solution, the linear advantage that full nodes get does not solve any scalability issue (especially so for thin nodes) and introduces the trust / security model problem that is in no way a trivial pedanticry. Commiting the ring signatures with an additional "full" hash for each block would alleviate that problem, but still trusts "anybody" stores the signatures.
And to add to all that, open source is not the holy grail in code vetting. I will name three issues from recent memory that had different direct causes, but the same primary cause:
1. Heartbleed
2. Shellshock
3. Block 202612
The primary cause is "just because anyone can do it doesn't mean anyone will do it", both in terms of open source vetting and in terms of storing the signatures. It is a tragedy of the commons.