I read your proposal, and could find no details about how a swarm client could actually divide up the task of verification of blocks. That or I simply didn't understand it.
It looks like a node picks a random number between 0 and N-1 and then checks transactions where id = tx-hash mod N.
For example, pool miners already don't have to verify blocks or transactions.
In fact, it would be much easier to write software that doesn't do it at all. Atm, the minting fee is much higher than the tx fees, so it is more efficient to just mint and not bother with the hassle of handling transactions.
If there is a 0.1% chance that a transaction is false, then including it in a block effectively costs the miner 25 * 0.1% = 0.025BTC, since if it is invalid, and he wins the block, the block will be discarded by other miners.
P2P pools would be better setup so that they don't risk it, until tx fees are the main source of income.
And we don't need swarm clients to "verify the blockchain", because all but the most recent has already been verified, unless you are starting up a fresh install of a full client. With light clients we can skip even that part, to a degree.
Having each new client verify a random 1% of the blocks would be a reasonable thing to do, if combined with an alert system. This would keep miners honest.