So, big players with big wallets and big transaction volumes will end up not paying any fees, whereas the small fish will have to pay fees. Is this a likely scenario, and if so is it a problem?
The outcome is the same as if they paid fees and included not their transactions into forged blocks.
I can see that is the case if the block would otherwise be full. In that case, putting your own transactions in and getting/paying zero fees means missing out on a bunch of other people's fees. But if the block you're forging isn't full then you are always best to include as many of your own transactions into your own forged blocks, so you get to perform fee-less transactions. Or is scaling done such that blocks would always be full, once nxt gets full momentum?