"Hashpoints" could be published by miners every so often (once a day maybe), so you'd only have to download the last day's transactions on a new client.
How would you verify that my transaction is valid as it spends an output that is 17 days old and you only have the transactions/blocks from the last 24 hours?
Why can't the client just start from the last verified blockchain hash?
Verified? By whom?
I think what you want is a slim client such as Multibit or Electrum.