Time is the flaw in your idea. If you had a really slow blockchain where new blocks were only appended every hour or so, perhaps then it could handle extreme compression. But the undeniable fact is that uncompressing such files takes time.
It also places an additional burden on memory requirements, so those securing the chain would need more powerful hardware to perform that task. If you limit the potential of who can secure your chain in that way, chances are, it won't be a very secure chain.
But if you could compress data and have easy access to the data you required at the same time, with just a small exchange of computation cost roughly proportional to the amount of data required, it would work no?
The idea of a blockchain is the nodes are constantly receiving new data. You won't have "easy access" to the recently sent transactions in order to validate and relay them if it takes time to unpack them first.
Compression may be viable for the initial sync, when your start a node for the first time and have to download the entire blockchain, but not for live day-to-day running.