you don't throw away the old blockchain. that's the whole point of blockchain, to have this immutable public distributed ledger where all the transactions from the start are stored in. if you throw it away then there is no way of verifying where coins came from.
I kid you not, some coins do it via snapshot, new blockchain is much smaller than the old one.
Maybe it's not the best example, because it's pretty young and unconventional coin, but IOTA did this multiple times... well, yeah, bad example because one of IOTA's feature is "no blockchain", but if you search you'll find some conventional, bitcoin-style coins that did snapshots.
it's just code so yeah it is possible.
I had beeen thinking it should be easy to implement this and your post confirms that.
Thanks!