Use a different browser. iCab Mobile supports uploading, downloading, and side-loading to DropBox or iDisk. The only time I use Safari is when I clock a link in Mail or Twitter or some other client; otherwise, I use iCab almost exclusively.
I agree that there are some issues with it (it crashes frequently enough that I care), but, overall, I've found, overall, it is much better.
Features I use daily:
* Pinboard current page
* ReadItLater current page
* Readability
* Side-load to DropBox to pick up on my Mac
* Youtube inside the browser
* Ad filters
And so on...