As best I can tell from what little info is available (noting that I was not a participant of Hack Day, or in any way part of the Hack cognoscenti), a primary difference between the free and premium API access will be that the free account APIs will not allow full email content access. I can only assume that this is to protect the revenue stream for premium features derived from full content access, e.g. email archive.
I can only assume that, in the short term, premium users represent so large a revenue source for Yahoo that it is willing to risk stifling long-term creativity. To be fair, it would be a difficult pro forma analysis: maximize the feature set available to developers who want to expand the utility of the platform vs. cannibalize current revenue streams. In a corporate setting, this is what we call a CLM.
Yet, from the sidelines, I would assert that if a user has already made a choice to use free accounts, it seems unlikely that they would switch to premium for any reason relevant to the APIs. (Ah, something my microeconomics prof lectured about is buzzing in my head...but I think I was asleep that day...) Wouldn't it be more likely that users from other mail services would migrate to Yahoo --- both free and premium --- if more creative and innovative services were available? If anyone from Yahoo would care to send me the data, I would gladly develop a predictive model, gratis. (Not holding my breath.)
It certainly may be that some of the premium services such as archival could be re-implemented by 3rd parties; I would assert that rather than eroding Yahoo's business, it would open new --- and most likely unexpected --- services that increase the attractiveness of the platform. Admittedly, this is only an opinion and would benefit from some number crunching. If I have a point here, it is this: has anyone at Yahoo crunched those numbers, or is it just that no one wants to speak out in the cathedral down in Sunnyvale?
"If you have the right attitude, interesting problems will find you." -Eric Steven Raymond