How much impact would mining rewards and halving have on the market then, when about 99% have already been mined and the remaining yet to be mined would not affect the market much.
Mining rewards have little to no impact on the market now, let alone then, it's often thought that selling pressure from miners brings the price down or the opposite, but IMO that is far from correct, the mining rewards are just a fraction of the trading volume, the supply from "elsewhere" is A LOT greater than what miners get as mining rewards, and as more and more coins leave the hands of miners to non-miners, this little impact miners have over the market slowly diminishes until it becomes completely irrelevant.
This is also a topic with many uncertainties about how motivated miners would be at that time to invest in mining rigs and electricity.
As long as there is any sort of profit to be made "big or small" some miners will still run their gears, in fact, even if running mining gear results in a loss, many people will still mine just to keep the blockchain alive (self-interest for them to be able to send and receive bitcoin), but the bigger issue would be the blockchain's security.
if the incentives to run a mining gear don't exist -- the network becomes more prone to attacks, so bitcoin's security as it stands right now is closely related to its value, the more expensive it gets the more secured it becomes, hopefully, that will change one day when the majority of people start using and protecting bitcoin rather than just mining it for profit.