What you are suggesting was proposed and discussed before, actually.
And the answer is no, this is not going to work nor solve the blockchain size problem.
First, if we are going to "store" an archived copy of the blockchain in a particular place then it can't be considered decentralized nor trustless system anymore.
I kind of knew this question would arrive and I was prepared for the same. The thing is we would not store it on one particular location but a group os 'trusted' locations.
Example: If we identify 50 or more trusted locations and store the archival there then it shouldn't be called centralized as the archival is still spread across trusted locations.
Second, each block is cryptographically linked to the previous block. Thus, if we need to validate a block/transaction a full node has to go all the way back to the genesis block.
=> we need full nodes, and we need more of them.
You can already prune your blockchain to less than 1 GB (AFAIK 550 MB was the minimum).
Yes, pruned blockchain does sort out the issue of storing the whole blockchain on your system however it still has to validate all the blocks until the genesis block.
Whereas my proposed system would eliminate the need to validate all the blocks until the genesis one and will only need to validate blocks until second genesis block/genesis block after archival whatever we name it.
If the size of the blockchain is the only concern in this discussion then instead of focusing on storing it elsewhere (which sounds more like centralization) focus on bitcoin transactions at byte level and see how you could "compress" them instead. FYI inside a transaction there are lots of wasted bytes that don't need to even exist. For your storage and even communication over P2P network you can come up with a compression technique that reduces the size by a lot.
I have actually been working on this recently and been able to "compress" a transaction up to 15%. That's just a start though, it needs a lot more work and study of other people's work to see what they have done, but you get the idea. With a block this can be more by simply dropping a lot of things and adding a "contract" in your compressor based on some factors such as block height. I expect the final result to be 30% compression.
Well that's a nice thing to start with. I haven't thought about it yet henceforth I can't comment on it. It's good that you have reached 15% compression and I hope you achieve more so that we all could get better at it.