I will not go too far in years and let discuss situation in year 2060 (42 years from now.) In these 42 years block reward will halved 11 times and block reward will be 12.5/211 or 12.5/2048 = .006BTC approx.
If I check Network difficulty, it seems to be increasing with each passing month (No volatility in Hash rate as opposed to price )
Since rewards are diminished so transaction fees will become main source of income .
If Network hash rate kept the same pace then for mining to be profitable , we are left with few possibilities.
1. Bitcoin price should go high or
2. Transaction fees should be more or
3. Hash rate reduction (Miners leaving the bitcoin Network)
Now exploring the possibility that Bitcoin price has gone high then it means the user that are paying in satoshies as transaction fees are paying more than the conventional system so there is no incentive to use bitcoin for transactions. Same logic is valid for if transaction fees become higher. We are now left with option of Hash rate reduction so that mining + transaction fees still remain profitable but hash rate reduction will only be possible if some miners stop mining(or leave the Network]. If miner start leaving the mining then difficulty will decrease but network now have few miners and make the system centralized instead of de centralized.
It look to me every thing like Decentralization,BTC price and transaction fees are all connected to each other and we should fix block reward as 1BTC if rewards goes below than 1 BTC,.
At first bitcoin was almost unknown, as time goes, it's name spreads widely. Now we have more than 16 million coin. As time goes, block reward reduces. Mining will be profitable in any way because miners need profit. As time goes, there are more bitcoin customers, less new coin. Supply is low, demand is high so here is the time of high price to make customers and manufacturers (miners) satisfied.
There is no need of high transaction fees because of what I said previously. And if miners leave bitcoin network, it won't solve a problem believe me and no one is going on market to leave opponents alone.