There are two ways to deal with this problem:
1) Force every user to submit PoW with their transactions, i.e. no transaction gets on the block chain without PoW attached. Note getting this sort of design to be robust, requires an entirely different way of structuring a block chain. If the attached PoW is low enough difficulty, then it costs more to farm it out (network latency cost) than to mine it locally given it is an insignificant and unnoticeable cost.
2) Limit debasement to a small annual percentage.
In that case, the professional miner will not be able to mine a significant quantity of the coins, and they will not be selling a significant percentage of the market cap. Thus the downward pressure on the price that impacts Bitcoin will be abated.
The reason for the block reward is to subsidise the security of the blockchain. In bitcoin, each transaction would need to pay $7 of transaction fees to achieve the level of security that it currently enjoys, without block reward.
Point 1 - if only transaction submitters can mine their own blocks, how do you handle difficulty adjustment?
Point 2 - If it is not profitable to mine the chain, how do you achieve the same level of security as with a subsidised chain?