Why all the negativity? It's clearly a deeply flawed idea but it's kinda fun to think about on a spring evening waiting for the game to start.
Here's my probably equally or more flawed idea - why not start with that as the baseline but allow teams to add available cap space to the contract? A team could even offer an incoming rookie a max contract (with typical "years in the league" downward adjustments) if they were that confident about it. With a max of one of these rookies a year and contracts so short, the fallout from overpaying a dud would be more limited than in the past, so let teams pay the players what they think they're worth.
I'm not really a fan of the idea of making it even more a bidding war. Teams hoarding cap space is already kind of an annoying feature of things, not dissimilar from tanking in a way -- string the fans along on the hope of signing a top free agent rather than the hope of a top draft pick. Having teams hoard cap space to offer huge contracts to highly touted prospects who have done nothing in the league yet seems even more obnoxious.
I would be in favor of allowing more room for negotiation of the terms of rookie deals, though, aside from the money. For example, maybe part of the intrigue of which guy signs where hinges on which team will give him four guaranteed years, as opposed to two guaranteed years plus two team option years.
Perhaps you could make it possible for players to "re-negotiate" their deals after a year or two, if they hit certain performance milestones (e.g. "1st Team All-Rookie," "All-NBA," "All-Star," "Rookie of the Year," "Most Improved Player," and so on). There could even be something similar to the arbitration system used in baseball, as an alternative to restricted free agency.
One possibility though, with regards to the money. Make the exception last for multiple years, similar to the Bi-Annual exception. A team could choose to use this year's exception, plus whatever else it had saved up from the year before, on a player it really likes. Or it could choose to save a sizable chunk of the exception from this year for next year's draft class.
Another wrinkle -- make it possible for teams to use the rookie exception space as a trade exception. If you're a contender, maybe you choose to pocket the Rookie Exception in order to acquire a necessary role player at some point during the season.