Those people who are cheap asses and don't want to pay ~1% fees can still pay less and have their blocks confirmed during off-peak hours.  And if that seems to be bad to you -- it's likely because you don't run a mining rig and pay for electricity to do so.  A $1400 Antminer S9 is about 1500watts.  A month of operation will run typically $120-$150ish in electricity costs in the USA.  The fact is, there's a cost involved in hashing.  And hashes are what secure the network.  You can't have your cake and eat it too.  You can't have a network that is as secure with far fewer hashes.  And you WILL have far fewer hashes if you make it impossible for miners to recoup their electricity costs.

As the mining subsidy halves every 4 years, miners will be relying more and more on the fees rather than that subsidy to recoup their costs.  By screwing them out of the mining fees (by removing competition for quick inclusion in the chain) it will make it impossible for them to recoup even their electricity fees, let alone their equip costs.  And that spells disaster because it means that they will either shut down the hashing or send their hashes to a competitor coin thereby making bitcoin less secure.  

As you can see from this graph, the subsidy has already mostly disappeared....and every four years, it keeps halving... That is built-into the system. It was expected that as the subsidy was removed, the miners would get paid by the fees as the network became more popular. Now you want to remove the vast majority of fees as well....not too smart AT ALL.