This looks basically like a "sidechain world" without main chain.

An advantage could be the easier handling of addresses. But all other problems and challenges of sidechains would also be present in that model.

For example, as ETFBitcoin already wrote, there is a danger that the different "shard tokens" could not be entirely fungible and instead convert into several different "coins". This could happen, for example, if one chain becomes notably weaker (has less support by miners) than the others, is thus less secure, and people (above all those waiting for high BTC amounts) could then desist to accept coins from addresses of that shard.

To avoid that, you would need a two-way peg mechanism that ensures that you always can change one coin of one shard to another shard. That could be more difficult than in a sidechain world, because an active coin in a sidechain has to be blocked in the main chain to avoid the supply being diluted, and thus there is always a main chain coin available for people wanting to exchange sidechain coins for it. In this proposal, however, this is not the case - you would have to force atomic swap servers to accept an 1:1 rate (and if they don't accept then they may simply reject swaps coming from shards they don't like).

In my opinion, if I understood the proposal correctly, then the drivechain proposal is less difficult to implement, and is also more flexible.