The likely result is transaction fees would go down to zero. So now how do you secure the net work in the absence of an emission?
The block reward subsidizes all transactions until it doesn't.
Then you pay to play. Maybe the miners include your transaction and maybe they don't. If they don't, then you offer a higher transaction fee. What's the issue?
The issue is that competition among the miners will drive the price down to zero since there is no longer scarcity in the blocksize, This effectively eliminates the difficulty in POW since there is no economic incentive to mine. The small block crowd do make a valid point here.
Edit: With no blocksize limit and no emission it is to the advantage of a miner to include all transactions regardless of fee price.
With no block reward and no blocksize limit, what's the advantage of including transactions that don't offer a transaction fee? What would happen if you just removed the blocksize limit. I want to see it tested. I don't think it'll be as bad as people think.