Right now, no matter how many mine, the block reward is the same.
Your formula would be difficult to implement and it's not future proof. After the last halving the miners will earn only from tx fees. How will you formula apply then? It won't. Sorry, IMHO it's not a good idea.
No more halving. The reward of bitcoins would be dynamic and thus the cap of 21 million would be lifted.
Many people argue that what gives Bitcoin its value is scarcity. If you make bitcoins cap we're removed it would lose that benefit. You're system would also need a cap at some point to eliminate the infinite supply concept. Even governments use manipulation of the supply of money to control inflation and deflation. Your system would be continuously inflationary.
If the adoption of bitcoin is not rapid enough, there won't be enough transaction fees to pay for the miner's electricity. But if it's too rapid, there won't be enough bitcoins for everyone (with the current system).
With my system, miners continue to earn bitcoins in perpetuity and more mining is encouraged and a growth that is too rapid is not a problem since the introduction of new bitcoins will be proportional to the growth.
Inflation is bad, but generally if it's less than 2% it's not a problem. The formula could be tweaked to achieve less than 2% inflation. Which even in an infinite time frame would be OK.
Bitcoin at it's inception had a 100% inflation ratio! The current inflation rate of bitcoin is about 4%/year, which is a bit high.
I'm giving you the benefit of the doubt believing your understanding of how Bitcoin works is limited. Yes, there could be a scenario where Bitcoin will not have enough continuous transactions to provide the overwhelming profit miners saw in the beginning. I'm not sure overwhelming profit is necessary to keep some people mining. Businesses, for example, that are making their living selling unique products for Bitcoin or are otherwise tied to Bitcoin may choose to mine for free or at a loss.
Bitcoin is divisible enough for everyone in the world to use it. There are 2.1 quadrillion units in Bitcoin. While that's not an infinite supply it should be enough to spread around 7 billion people. In roughly seven years Bitcoin will be down to a 3btc block reward and mostly all mined into existence. There will be almost no inflation as no new money will be added to the money supply.
The only benefit you see from an increased mining reward is your ability to collect coins at a faster rate than you can now. The problem with that theory is that all of the extra coins you collect will be worth less than the few you can collect now because of the increase in the money supply. Essentially, you will end up right back where you started.