Error correction is an interesting suggestion.
If there was 10000 nodes and each stored 0.1% of the blocks, at random, then the odds of a block not being stored is 45 in a million.
Blocks are stored on average 10 times, so there is already reasonable redundancy.
With 1 million blocks, 45 would be lost in that case, even though most are stored multiple times.
With error correction codes, the chances of blocks going missing is much lower.
For example, if there was 32 out of 34 Reed-Solomon-like system, then 2 blocks out of 34 could be lost without any actual data loss for the network.
As a back of the envelop check, the odds of 2 missing blocks landing within 34 of another is 68/1000000. That means that the odds of 2 missing blocks falling in the same correction section is 45 * 34 / 1000000 = 0.153%. Even in that case, the missing blocks could be reconstructed, as long as you know that they are missing.
The error correction code has taken it from being a near certainty that some blocks would be lost to less than 0.153%.
A simple error correction system would just take 32 blocks in sequence and then compute 2 extra blocks.
The extra blocks would have to be the same length as the longest block in the 32 being corrected.
The shorter blocks would be padded with zeroes so everything is the same size.
For each byte position in the blocks you compute the polynomial that goes through byte (x, data(x)), for x = 0 to 31. This could be a finite field, or just mod 257.
You can then compute the value for x=32 and x = 33. Those are the values for the 2 extra blocks.
If mod 257 is used, then only the 2 extra blocks have to deal with symbols from 0 to 256.
If you have 32 of the 34 blocks, you can compute the polynomial and thus generate the 32 actual blocks.
This could be achieved by a soft fork by having a commitment every 32 blocks in the coinbase.
It makes the header chain much longer though.
Longer sections are more efficient, but need more calculations to recover everything. You could also do interleaving to handle the case where entire sections are missing.