I'm a new player, so I'm not that familiar with the economy of this game at this point just yet.
I'm not sure how the current inflation compares to the beginning of the game. Eventually when numbers are high, percentual inflation drops but inflation will still rise linearly. I mean, if right now the price of shaman changes from 800 to 880 bfp, that's a 10% increase which doesn't sound like much. But if it increased from 90 to 170 at the beginning of the game, that's almost a 100% price increase even though it's the exact same price increase (80bfp).
While right now people might indeed have too many cards, the ones that need cards don't have that much funds I imagine (newer players). I understand keeping the game free to play, but that does indeed mean that there will be an infinite supply of cards and eventually, given enough time, everyone will have every card including promo's (except newer players). So the auction market right now kind of sucks for newer players since they have a low amount of cards, but card packs ALSO aren't that enticing of an option due to a somewhat high price.
The only real solution I can see for this is constant updates with new cards, since that gives a new BFP sink to give money to. And I know this is not an easy option, but sustainability is quite hard in an environment that doesn't change much and continues "printing" it's own money. Like the OP said, in the old game influx of BFP was lower due to the barrier that it costs real money. Besides, 2 updates came out during the lifetime of Battleforge, creating 2 new money sinks.
But with all thats said, I'm also sure that this is what the open beta also tackles. Seeing how the economy evolves and perhaps making adjustments accordingly. I have full faith in the developers and I will start grinding away. This is just my 2 cents, take it as you will. Have a nice day!