About the only reason that Fannie/Freddie as fully public entities might not have led to the corruption and scandals which happened there would be that a fully government-run entity wouldn't have the profit motive as a reason to subvert their oversight (the term "regulation" would really no longer apply in that case) since the civil-service pay structure would be unlikely to include performance bonuses for those at the top.

As for the privatize profits/dump losses on the taxpayers dichotomy that we have now, half of that would still exist and there would be no profits to be shared over any group. A big part of why these organizations were made semi-private to begin with was because of the drag on the budget resulting from their operating losses as fully government-run entities. The analogy I saw elsewhere was that Fannie and Freddie became off balance sheet entities of the U.S. Gov't in order to hide the associated liabilities on paper without actually getting rid of them in reality.

I'd guess that a fully public version of these entities might not have bought nearly as much subprime debt (unless the pols who set policy and loved the "affodability of homeownership" angle of subprime lending in the beginning decided that was a desirable policy), but in the beginning there was no shortage of fully private buyers for those bonds; hedge funds and European investment/institutional banks were gobbling them up as fast as they could be bundled not to mention fixed-income mutual funds and pension plans. In the end, this issue will probably be a red herring since Bernanke and Paulson have pretty much committed to shifting large chunks of this bad paper onto the books of the U.S. Treasury anyway.