I'd rather see an asset than another chain...
That's a fair point. With the strong deflationary priority they might be worried that BTS isn't a sound foundation, but it would be easy enough to fork off if Bitshares ever seemed in danger of hyper-inflationary collapse.
That would save them the overhead of a full new chain and new set of delegates
What does and expansion or contraction of the BTS supply have to do with the supply or price of an asset on the platform?
The people behind Rand Paul Coin clearly view an expandable supply with greater suspicion than we do. If Bitshares somehow hyperinflated to the point of total loss of confidence and value, then delegates would have no incentive. User issued assets would then be frozen until they could be migrated to a living chain.
Obviously I don't think that would happen, but they probably do, or they wouldn't be forking.
Edit: So the answer to your question is: Absolutely nothing, unless Bitshares collapsed entirely.