Hey man, so hopefully I can address some of the concerns you're having. First of all, you're correct in that Proving Grounds as-is is not a faithful representation of classic ARAM gameplay. We took elements of what we enjoyed from both ARAM and ARAB and adapted them to an existing map; the result is that it's something that's similar, but still quite different, but what we hope is an improvement from ARAM and ARAB.
To address your concerns piecemeal, I'm going to refer to Proving Grounds as PG, classic ARAM as ARAM, and ARAB on Dominion as ARAB. Some of the justifications have already been covered by the other posters, so I'll focus on what's not been mentioned.
Health relics, along with brush, are both elements intended to give the otherwise straightforward terrain of Proving Grounds some deeper gameplay. On ARAM, there's the notion of two distinct fronts. You've got purple team in a line parallel to blue, and this is the default configuration until someone initiates or gets caught. While there's certainly merit to this gameplay, it does marginalize the usefulness of melee champs and amplifies the effectiveness of ranged pokers and AoE champs (say, Xerath and Ashe respectively). What we did on PG is break these fronts; you've got champs vying for brush control and scrambling for health relics. It's an ongoing process that keeps the state of both teams quite volatile and provides a lot of openings to capitalize on mistakes.
Increased Starting Gold
This was a decision made very early in the project, and it directly relates to the melee/ranged disparity and the general feeling players have when they're "stuck" in battle. To clarify on this, it's when you're low health with no sustain; too low to properly fight, but you don't want to feed your opponents a free kill. Increased starting gold gives players the ability purchase enough sustain or survivability to mitigate this issue, though not enough to solve it. In addition, it allows for a much higher variety in starting builds.
I actually have to go do something right now, but I'll be back to answer the rest of the points. Please note that we do plan to support Proving Grounds; both Brackhar and I will be providing short term support, and I'll actually be jumping onto the live team for the conceivable future to provide long-term support for not just Proving Grounds, but other non-SR maps as well. It's also possible that we add a "classic" mode to the map in the future that removes the health relics, ambient gold and experience, and sets you back to level 1. But for now, I (and the PG team) implore you to play the map as-is and give us your feedback.