The problem is, doing this will cause everyone to have to do it, relays to fill up even more with duplicate messages and waste bandwidth. Normal clients will be swamped UNLESS they use these relay aggregators. Then they will all connect to the aggregator(s), then we're centralized. I hope we can come up with better solutions before that happens because the freedom nostr gives us is to move to other relays if we get kicked, and for anyone to run a low-cost node in the system (decentralization/anti-censor). Currently the source code for aggregation is all closed source, so you're supporting a system that will ultimately either use you as the product, cost a lot more than it does now, or will fail. The only open-source part of this list is blastr, which is a write-only blast to all known relays (not an aggregator).
Discussion
I totally agree with you, this solution I have proposed is to avoid headaches with relays and save on battery and data, but the solution is the Gossip model that solves all the problems cited by you.
The ideal would be for me to have my private relay and store my notes there and the client would be smart and be able to fetch my notes from my relay, this would make the network much more scalable.
Unfortunately at the moment except for gossip no one is going in this direction.
I think I read somewhere coracle is doing gossip now too.. Just a matter of time. I have a feeling, aggregators might be SOL once Auth is implemented for relays. Even a free auth, like solve a captcha or etc and all of a sudden this model of leaching off the relays doesn't work so well.