Could a Multi-Chain Bitcoin Help the issue of Scaling?
No, I don't think that sharding is as simple or beneficial as portrayed here. Here are a few thoughts:

Splitting by addresses doesn't seem plausible. Most transactions have either multiple inputs or multiple recipients. It's not clear how transactions would be handled that attempt to spend funds from both chains or pay to both chains. If they need to be present on each chain, I don't think we'd get a significant traffic reduction on either chain. If they do get included on both sides, how do we ensure that they don't get confirmed on only one side? If they can only be included on one side, how do we coordinate that?
ETH has been working on Sharding since 2016(?), and as far as I can tell, it requires layers of mitigations and complexity, and comes with all sorts of trade-offs. ETH requires global state for each transaction's execution. By introducing sharding, ETH gets multithreaded validation. Bitcoin's transactions are inherently stateless, and its scalability concerns are related to total resource usage. Two shards of 0.5 MB blocks are no better than one chain with 1 MB blocks for that. Two shards with 0.5 MB blocks that have a storage footprint of 0.75 MB and coordination overhead sound like a step back.
It sounds like a complete consensus overhaul. It's unlikely that people would be comfortable to support such a proposal.

That said, we already have some sidechains and second layer solutions that we can offload transaction traffic to with far less overhead or critical changes.