Basically no one would mine then.
They would mine for the fees.
Ok then 99.5% won't mine. Network security would fall massively and it would be trivial to double spend the network. The "coins" only have value because they have utility (impossible to counterfeit, and very difficult to "reverse" once confirmed). No utility = no value and the price rapidly crashes to zero (this would have a compounding effect as not only would the compensation paid to miners drop 99% in BTC terms the falling exchange rate would mean in USD/EUR terms the compensation would fall 99.99%+).
Satoshi always intended "minting" to not only solve the initial distribution problem but to acts as a subsidy. The subsidy keeps fees low while the network grows. Another way to look at it is right now fees make up about 1% of total miner compensation. This means everything else being equal to purchase the same amount of security tx volume would either need to be 100x as high or the average fee per tx would need to be 100x as high. Neither of those are realistic. Even with rapid organic growth we are probably many years from such tx volume, and raising fees to be $5 to $10 per tx would cripple utility and adoption. The (declining) subsidy gives the network time to grow the the volume levels where fees would make it self sufficient.
The subsidy "buys" 99%+ of the security that is available today. You can't remove 99% of the compensation to miners and expect anything other than security falling 99% (or more).
That way the initial distribution of coins is garantueed to be fair for everyone, since the coins are going to the actual users of the network (which includes also 'the poor'), instead of the big guys.
Actually as proposed it would be very easy to game. The subsidy protects the network but it also serves the purpose of being hard to "game". Please describe in exact details how you would distribute 25 BTC "randomly" in such a manner that it would be fair. Hint: if you could solve that problem (sybil attack) you wouldn't need mining at all. Using the same logic nodes would simply determine the fairest sequence of transactions (i.e. instant confirmations with no cost, delay, or fraud).
And to discourage users from spamming the chain with dummy transactions, the reward should be equal (or lower) than the total amount of fees paid in the block. This causes their EV (expected value) to stay the same, rendering spam useless.
This is an even worse "solution" security of the network would fall off massively or miners would simply demand much higher fees in compensation. Miners could still game this by including all "real" high fee txs and then filling the block with tx back to addresses controlled by the miner (with high fees = going right back to miner anyways). Miners could set the reward to be whatever they wanted possibly even higher than the current reward. Of course lower fee and free tx would never be included in a block, you just created a penalty that punishes miners for including those txs (by directly lowering their gross revenue).