Ignoring the practical difficulty of making any such radical change to bitcoin, there would be profound negative consequences from such a change. Eliminating the block reward would almost certainly make mining less profitable.
After all, the block reward is a huge part of mining revenue. Eliminating the block reward would eliminate that portion of the revenue. There doesn't seem to be any obvious reason to expect it to be possible for transaction fees to be able to increase to compensate.
Bitcoin's security is dependent on how much it would cost to create a longer chain. If miners make less money in aggregate, they will do less hashing in aggregate. That means it would cost an attacker less money to outmine the miners. This means bitcoin would be more vulnerable to 51% attacks.
Now, consider two numbers:
X = The cost to attack bitcoin
Y = The amount of money you can make by attacking bitcoin
If Y ever exceeds X, bitcoin breaks. You are suggesting reducing X. That necessarily means that either somehow Y will have to be reduced as well, something else will have to be done to increase X, or both.
How can X be increased? Probably only by waiting for more confirmation and slowing down the blockchain. But that won't be enough by itself.
So how can Y go down? Effectively, it has to mean that the value of bitcoin and the value of the transactions that occur on the chain have to go down. If the whole bitcoin ecosystem is only churning $1 million a day, an attack will be much less lucrative than one that is churning $1 billion a day.